Edit Profile (opens in new tab) Oden, John Tinsley Compute Distance To: Compute Author ID: oden.john-tinsley Published as: Oden, J. T.; Oden, J. Tinsley; Oden, John Tinsley; Oden, Tinsley; Oden, Tinsley J.; Tinsley Oden, J.; Oden, T.; Oden more...less External Links: MGP · Wikidata · dblp · GND · IdRef Documents Indexed: 318 Publications since 1966, including 20 Books 30 Contributions as Editor · 4 Further Contributions Biographic References: 4 Publications Co-Authors: 141 Co-Authors with 274 Joint Publications 3,327 Co-Co-Authors all top 5 Co-Authors 56 single-authored 37 Prudhomme, Serge 29 Demkowicz, Leszek F. 15 Babuška, Ivo 12 Ainsworth, Mark 10 Zienkiewicz, Olgierd Cecil 9 Carey, Graham Francis 9 Kikuchi, Noboru 9 Lima, Ernesto A. B. F. 9 Wellford, Landon Carter jun. 8 Argyris, John Hadji 8 Bass, Jon M. 8 Feng, Yusheng 8 Gallagher, Richard Hugo 8 Martins, João A. C. 8 Reddy, Junuthula Narasimha 7 Bauman, Paul T. 7 Devloo, Philippe Remy Bernard 7 Hughes, Thomas J. R. 7 Pires, E. B. 7 Rachowicz, Waldemar 7 Wohlmuth, Barbara I. 6 Almeida, Regina C. 6 Baumann, Carlos Erik 6 Becker, Eric B. 6 Chamoin, Ludovic 6 Patra, Abani K. 6 Romkes, Albert 6 Strouboulis, Theofanis 6 Vemaganti, Kumar S. 5 Bhandari, Dev R. 5 Cho, Jin-Rae 5 Dhia, Hachmi Ben 5 Faghihi, Danial 5 Jacquotte, Olivier-Pierre 5 Wu, Weihan 5 Yankeelov, Thomas E. 4 Campos, L. T. 4 Doltsinis, Ioannis St. 4 Fritz, Marvin 4 Hawkins-Daarud, Andrea J. 4 Jha, Prashant K. 4 Le Tallec, Patrick 4 Tworzydlo, Wlodzimierz W. 4 Westermann, T. A. 4 Zohdi, Tarek I. 3 Bernadou, Michel 3 Bey, Kim S. 3 Brauchli, Hans J. 3 Duarte, Carlos Armando 3 Fuentes, David 3 Legat, Vincent 3 Moës, Nicolas 3 Prudencio, Ernesto E. 3 Reddy, C. T. 3 Taylor, Cedric 3 van der Zee, Kristoffer George 2 Belytschko, Ted Bohdan 2 Berry, C. W. 2 Botkin, Mark E. 2 Cao, Lianghao 2 Elkhodja, Nadia 2 Farrell, Kathryn 2 Flaherty, Joseph E. 2 Fost, R. B. 2 Guermond, Jean-Luc 2 Hardy, O. 2 Hormuth, David A. II 2 Johnson, C. Philip 2 Karafiat, Andrzej 2 Köppl, Tobias 2 Ladevèze, Pierre 2 Nobile, Fabio 2 Papadrakakis, Manolis 2 Pattani, Paresh 2 Rabier, Patrick J. 2 Rahman, Mohammad Mamunur 2 Rylander, Marissa Nichole 2 Scarabosio, Laura 2 van de Geijn, Robert Alexander 2 Whiteman, John Robert 1 Akay, Hasan U. 1 Alduncin, Gonzalo 1 Bajaj, Chandrajit L. 1 Barros, Felício Bruzzi 1 Bauman, Patricia E. 1 Biduat, L. 1 Bischoff, Dieter Ernst 1 Bouclier, Robin 1 Brand, G. F. 1 Browne, James C. 1 Chen, Wanji 1 Chien, Weizang 1 Ciarlet, Philippe Gaston 1 Coffignal, G. 1 Constantinescu, Andrei 1 Cornett, D. 1 Craig, Roy R. jun. 1 de Arantes Oliveira, E. R. 1 de Campos, L. T. 1 Deb, Manas K. ...and 72 more Co-Authors all top 5 Serials 88 Computer Methods in Applied Mechanics and Engineering 19 International Journal for Numerical Methods in Engineering 18 International Journal of Engineering Science 10 Computers & Mathematics with Applications 8 Journal of Computational Physics 8 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 7 Numerical Methods for Partial Differential Equations 6 Nonlinear Analysis. Theory, Methods & Applications 5 AIAA Journal 5 Computers and Structures 5 International Journal of Solids and Structures 4 International Journal for Numerical Methods in Fluids 4 Computational Mechanics 3 Journal of Computational and Applied Mathematics 3 SIAM Journal on Numerical Analysis 3 Applied Numerical Mathematics 3 Finite Elements in Analysis and Design 3 SIAM Journal on Scientific Computing 2 International Journal of Non-Linear Mechanics 2 Numerical Functional Analysis and Optimization 2 Quarterly of Applied Mathematics 2 Physica D 2 Communications in Applied Numerical Methods 2 Journal of Elasticity 2 Archives of Computational Methods in Engineering 2 Universitext 1 Journal of Applied Mechanics 1 Journal of the Franklin Institute 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Biology 1 Journal of the Mechanics and Physics of Solids 1 Journal of Sound and Vibration 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Numerische Mathematik 1 Advances in Applied Mathematics 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Pokroky Matematiky, Fyziky & Astronomie 1 SIAM Journal on Mathematical Analysis 1 Journal de Mécanique Théorique et Appliquée 1 Communications in Numerical Methods in Engineering 1 Revue Européenne des Éléments Finis 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Journal of Mathematical Fluid Mechanics 1 Nonlinear Analysis. Real World Applications 1 Matematicheskoe Modelirovanie 1 Multiscale Modeling & Simulation 1 Acta Numerica 1 International Journal of Numerical Analysis and Modeling 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Lecture Notes in Mathematics 1 SIAM Studies in Applied Mathematics 1 Studies in Applied Mechanics 1 International Journal for Numerical Methods in Biomedical Engineering 1 Research in the Mathematical Sciences 1 Textbooks in Mathematics 1 Pure and Applied Mathematics. A Wiley-Interscience Series of Texts, Monographs and Tracts 1 Wiley Series in Computational Mechanics all top 5 Fields 200 Mechanics of deformable solids (74-XX) 149 Numerical analysis (65-XX) 92 Fluid mechanics (76-XX) 61 Partial differential equations (35-XX) 44 Calculus of variations and optimal control; optimization (49-XX) 39 General and overarching topics; collections (00-XX) 20 Biology and other natural sciences (92-XX) 13 Mechanics of particles and systems (70-XX) 11 Operator theory (47-XX) 9 Statistics (62-XX) 9 Statistical mechanics, structure of matter (82-XX) 8 Functional analysis (46-XX) 5 Approximations and expansions (41-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 History and biography (01-XX) 3 Measure and integration (28-XX) 3 Ordinary differential equations (34-XX) 3 Probability theory and stochastic processes (60-XX) 2 Quantum theory (81-XX) 2 Operations research, mathematical programming (90-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 301 Publications have been cited 8,849 times in 5,806 Documents Cited by ▼ Year ▼ Contact problems in elasticity: A study of variational inequalities and finite element methods. Zbl 0685.73002Kikuchi, N.; Oden, J. T. 853 1988 A posteriori error estimation in finite element analysis. Zbl 1008.65076Ainsworth, Mark; Oden, J. Tinsley 738 2000 An \(h\)-\(p\) adaptive method using clouds. Zbl 0918.73328Duarte, C. Armando; Oden, J. Tinsley 304 1996 An introduction to the mathematical theory of finite elements. Zbl 0336.35001Oden, J. T.; Reddy, J. N. 246 1976 A posteriori error estimation in finite element analysis. Zbl 0895.76040Ainsworth, Mark; Oden, J. Tinsley 241 1997 Finite elements of nonlinear continua. Zbl 0235.73038Oden, J. T. 220 1972 A discontinuous \(hp\) finite element method for convection-diffusion problems. Zbl 0924.76051Baumann, Carlos Erik; Oden, J. Tinsley 212 1999 A discontinuous \(hp\) finite element method for diffusion problems. Zbl 0926.65109Oden, J. Tinsley; Babuška, Ivo; Baumann, Carlos Erik 205 1998 \(H\)-\(p\) clouds – an \(h\)-\(p\) meshless method. Zbl 0869.65069Duarte, C. Armando; Oden, J. Tinsley 201 1996 A unified approach to a posteriori error estimation using element residual methods. Zbl 0797.65080Ainsworth, Mark; Oden, J. Tinsley 169 1993 A new cloud-based \(hp\) finite element method. Zbl 0956.74062Oden, J. T.; Duarte, C. A. M.; Zienkiewicz, O. C. 160 1998 Solution of stochastic partial differential equations using Galerkin finite element techniques. Zbl 1075.65006Deb, Manas K.; Babuška, Ivo M.; Oden, J. Tinsley 158 2001 Toward a universal h-p adaptive finite element strategy. I: Constrained approximation and data structure. Zbl 0723.73074Demkowicz, L.; Oden, J. T.; Rachowicz, W.; Hardy, O. 153 1989 On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors. Zbl 0945.65123Prudhomme, S.; Oden, J. T. 144 1999 Goal-oriented error estimation and adaptivity for the finite element method. Zbl 0987.65110Oden, J. T.; Prudhomme, S. 140 2001 Models and computational methods for dynamic friction phenomena. Zbl 0567.73122Oden, J. T.; Martins, J. A. C. 139 1985 Toward a universal h-p adaptive finite element strategy. II: A posteriori error estimation. Zbl 0723.73075Oden, J. T.; Demkowicz, L.; Rachowicz, W.; Westermann, T. A. 138 1989 A discontinuous \(hp\) finite element method for the Euler and Navier-Stokes equations. Zbl 0985.76048Baumann, Carlos Erik; Oden, J. Tinsley 110 1999 Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. I: Error estimates and adaptive algorithms. Zbl 0992.74072Oden, J. Tinsley; Vemaganti, Kumar S. 102 2000 General diffuse-interface theories and an approach to predictive tumor growth modeling. Zbl 1186.92024Oden, J. Tinsley; Hawkins, Andrea; Prudhomme, Serge 96 2010 Toward a universal h-p adaptive finite element strategy. III: Design of h-p meshes. Zbl 0723.73076Rachowicz, W.; Oden, J. T.; Demkowicz, L. 82 1989 Numerical simulation of a thermodynamically consistent four-species tumor growth model. Zbl 1242.92030Hawkins-Daarud, Andrea; van der Zee, Kristoffer G.; Oden, J. Tinsley 81 2012 Variational methods in theoretical mechanics. Zbl 0324.73001Oden, J. T.; Reddy, J. N. 80 1976 Estimation of modeling error in computational mechanics. Zbl 1053.74049Oden, J. Tinsley; Prudhomme, Serge 74 2002 Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws. Zbl 0672.73079Martins, J. A. C.; Oden, J. T. 70 1987 On the calculation of consistent stress distributions in finite element approximations. Zbl 0251.73056Oden, J. T.; Brauchli, H. J. 60 1971 Qualitative methods in nonlinear mechanics. Zbl 0578.70001Oden, J. Tinsley 59 1986 A posteriori error estimators for the Stokes and Oseen equations. Zbl 0879.65067Ainsworth, Mark; Oden, J. Tinsley 56 1997 \(hp\)-version discontinuous Galerkin methods for hyperbolic conservation laws. Zbl 0894.76036Bey, Kim S.; Oden, J. Tinsley 56 1996 Finite elements. Mathematical aspects. Zbl 0496.65055Oden, J. Tinsley; Carey, Graham F. 56 1983 Finite elements. Computational aspects. Zbl 0558.73064Carey, Graham F.; Oden, J. Tinsley 55 1984 Multiscale modeling of physical phenomena: adaptive control of models. Zbl 1126.74006Oden, J. Tinsley; Prudhomme, Serge; Romkes, Albert; Bauman, Paul T. 54 2006 Hierarchical modeling of heterogeneous bodies. Zbl 0921.73080Zohdi, Tarek I.; Oden, J. Tinsley; Rodin, Gregory J. 54 1996 Theory of variational inequalities with applications to problems of flow through porous media. Zbl 0444.76069Oden, J. T.; Kikuchi, N. 53 1980 On the application of the Arlequin method to the coupling of particle and continuum models. Zbl 1252.74055Bauman, Paul T.; Ben Dhia, Hachmi; Elkhodja, Nadia; Oden, J. Tinsley; Prudhomme, Serge 51 2008 Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems. Zbl 0382.65056Babuška, Ivo; Oden, J. T.; Lee, J. K. 50 1977 A procedure for a posteriori error estimation for \(h\)-\(p\) finite element methods. Zbl 0778.73060Ainsworth, Mark; Oden, J. Tinsley 49 1992 Finite element methods for constrained problems in elasticity. Zbl 0486.73068Oden, J. T.; Kikuchi, N. 49 1982 A discontinuous \(hp\) finite element method for diffusion problems: 1-D analysis. Zbl 0940.65076Babuška, I.; Baumann, C. E.; Oden, J. T. 48 1999 Finite elements. An introduction. Vol. I. Zbl 0459.65070Becker, Eric B.; Carey, Graham F.; Oden, J. Tinsley 48 1981 A general theory of finite elements. II: Applications. Zbl 0263.73048Oden, J. Tinsley 48 1969 An a posteriori error estimate for finite element approximations of the Navier-Stokes equations. Zbl 0844.76056Oden, J. Tinsley; Wu, Weihan; Ainsworth, Mark 47 1994 Nonlocal and nonlinear friction laws and variational principles for contact problems in elasticity. Zbl 0515.73121Oden, J. T.; Pires, E. B. 47 1983 On an h-type mesh-refinement strategy based on minimization of interpolation errors. Zbl 0556.73081Demkowicz, L.; Devloo, Ph.; Oden, J. T. 47 1985 Mathematical perspectives on large eddy simulation models for turbulent flows. Zbl 1094.76030Guermond, J.-L.; Oden, J. T.; Prudhomme, S. 45 2004 Accuracy estimates and adaptive refinements in finite element computations. Lectures presented at the international conference held in Lisbon, June 1984. Zbl 0663.65001 44 1986 Penalty-finite element methods for the analysis of Stokesian flows. Zbl 0478.76041Oden, J. Tinsley; Kikuchi, Noboru; Song, Young Joon 42 1982 Adaptive finite element methods for the analysis of inviscid compressible flow: I: Fast refinement/unrefinement and moving mesh methods for unstructured meshes. Zbl 0593.76080Oden, J. T.; Strouboulis, T.; Devloo, P. 42 1986 A posteriori error estimators for second order elliptic systems. II: An optimal order process for calculating self-equilibrating fluxes. Zbl 0789.65083Ainsworth, M.; Oden, J. T. 41 1993 Analysis and adaptive modeling of highly heterogeneous elastic structures. Zbl 0924.73015Oden, J. Tinsley; Zohdi, Tarek I. 41 1997 Finite elements. Vol. II: A second course. Zbl 0515.65075Carey, Graham F.; Oden, J. Tinsley 41 1983 Hierarchical modeling of heterogeneous solids. Zbl 0972.74014Oden, J. Tinsley; Vemaganti, Kumar; Moës, Nicolas 40 1999 Estimation of local model error and goal-oriented adaptive modeling of heterogeneous materials. II: A computational environment for adaptive modeling of heterogeneous elastic solids. Zbl 1030.74051Vemaganti, Kumar S.; Oden, J. Tinsley 40 2001 An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable. Zbl 0601.65081Demkowicz, L.; Oden, J. T. 40 1986 Adaptive finite elements for flow problems with moving boundaries. I. Variational principles and a posteriori estimates. Zbl 0583.76025Demkowicz, L.; Oden, J. T.; Strouboulis, T. 38 1984 Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws. Zbl 0679.73050Martins, J. A. C.; Oden, J. T. 37 1987 An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in two space variables. Zbl 0602.76097Demkowicz, L.; Oden, J. T. 35 1986 Bayesian calibration, validation, and uncertainty quantification of diffuse interface models of tumor growth. Zbl 1280.35163Hawkins-Daarud, Andrea; Prudhomme, Serge; van der Zee, Kristoffer G.; Oden, J. Tinsley 35 2013 Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method. Zbl 1159.74303Prudhomme, S.; Ben Dhia, H.; Bauman, P. T.; Elkhodja, N.; Oden, J. T. 34 2008 Selection and assessment of phenomenological models of tumor growth. Zbl 1301.92034Oden, J. Tinsley; Prudencio, Ernesto E.; Hawkins-Daarud, Andrea 33 2013 Verification and validation in computational engineering and science: basic concepts. Zbl 1198.74126Babuska, Ivo; Oden, J. Tinsley 31 2004 Applied functional analysis. Zbl 0851.46001Oden, J. Tinsley; Demkowicz, Leszek F. 31 1996 Adaptive multiscale modeling of polymeric materials with Arlequin coupling and goals algorithms. Zbl 1229.74006Bauman, Paul T.; Oden, J. Tinsley; Prudhomme, Serge 31 2009 Clouds, cracks and FEM’s. Zbl 0976.74071Oden, J. T.; Duarte, C. A. 30 1997 A priori error estimate for the Baumann-Oden version of the discontinuous Galerkin method. Zbl 1007.65084Prudhomme, Serge; Pascal, Frédéric; Oden, J. Tinsley; Romkes, Albert 29 2001 A numerical analysis of a class of contact problems with friction in elastostatics. Zbl 0504.73050Campos, L. T.; Oden, J. T.; Kikuchi, N. 28 1982 Local a posteriori error estimators for variational inequalities. Zbl 0768.65032Ainsworth, Mark; Oden, J. Tinsley; Lee, C. Y. 28 1993 On dual-complementary variational principles in mathematical physics. Zbl 0273.49066Oden, J. T.; Reddy, J. N. 28 1974 An interpretation of the Navier-Stokes-alpha model as a frame-indifferent Leray regularization. Zbl 1082.35120Guermond, J. L.; Oden, J. T.; Prudhomme, S. 28 2003 An h-p adaptive finite element method for the numerical simulation of compressible flow. Zbl 0636.76064Devloo, Philippe; Oden, J. Tinsley; Pattani, Paresh 27 1988 Analysis of hourglass instabilities and control in underintegrated finite element methods. Zbl 0543.73104Jacquotte, O.-P.; Oden, J. Tinsley 27 1984 Variational methods in theoretical mechanics. 2nd ed. Zbl 0518.73010Oden, J. T.; Reddy, J. N. 26 1983 \(hp\)-version discontinuous Galerkin methods for hyperbolic conservation laws: A parallel adaptive strategy. Zbl 0855.65106Bey, Kim S.; Patra, Abani; Oden, J. Tinsley 25 1995 A parallel \(hp\)-adaptive discontinuous Galerkin method for hyperbolic conservation laws. Zbl 0860.65094Bey, Kim S.; Oden, J. Tinsley; Patra, Abani 25 1996 On some existence and uniqueness results in contact problems with nonlocal friction. Zbl 0511.73122Demkowicz, L.; Oden, J. T. 25 1982 A hybrid ten-species phase-field model of tumor growth. Zbl 1404.35459Lima, E. A. B. F.; Oden, J. T.; Almeida, R. C. 25 2014 Adaptive \(hpq\)-finite element methods of hierarchical models for plate- and shell-like structures. Zbl 0892.73068Oden, J. Tinsley; Cho, J. R. 24 1996 Stability of some mixed finite element methods for Stokesian flows. Zbl 0598.76033Oden, J. Tinsley; Jacquotte, Olivier-Pierre 24 1984 A new finite element method for solving compressible Navier-Stokes equations based on an operator splitting method and h-p adaptivity. Zbl 0731.76041Demkowicz, L.; Oden, J. T.; Rachowicz, W. 24 1990 Research directions in computational mechanics. Zbl 1025.74503Oden, J. Tinsley; Belytschko, Ted; Babuska, Ivo; Hughes, T. J. R. 24 2003 High-order Taylor-Galerkin and adaptive \(h\)-\(p\) methods for second-order hyperbolic systems: Application to elastodynamics. Zbl 0767.73077Safjan, A.; Oden, J. Tinsley 23 1993 A priori error analyses of a stabilized discontinuous Galerkin method. Zbl 1058.65122Romkes, A.; Prudhomme, S.; Oden, J. T. 23 2003 Selection, calibration, and validation of models of tumor growth. Zbl 1349.92075Lima, E. A. B. F.; Oden, J. T.; Hormuth, D. A. II; Yankeelov, T. E.; Almeida, R. C. 22 2016 A parallel adaptive strategy for \(hp\) finite element computations. Zbl 0851.73067Oden, J. T.; Patra, Abani 22 1995 A posteriori error analysis in finite elements: The element residual method for symmetrizable problems with applications to compressible Euler and Navier-Stokes equations. Zbl 0727.73072Oden, J. T.; Demkowicz, L.; Rachowicz, W.; Westermann, T. A. 22 1990 Solution of elastic scattering problems in linear acoustics using \(h\)-\(p\) boundary element method. Zbl 0778.73081Demkowicz, L.; Karafiat, A.; Oden, J. Tinsley 21 1992 Parallel domain decomposition solver for adaptive \(hp\) finite element methods. Zbl 0890.65124Oden, J. T.; Patra, Abani; Feng, Yusheng 21 1997 Numerical analysis of certain contact problems in elasticity with non- classical friction laws. Zbl 0499.73091Oden, J. T.; Pires, E. B. 21 1983 Numerical analysis of finite axisymmetric deformations of incompressible elastic solids of revolution. Zbl 0194.26303Oden, J. T.; Key, J. E. 20 1970 A posteriori error estimation of \(h-p\) finite element approximations of frictional contact problems. Zbl 0847.73062Lee, C. Y.; Oden, J. T. 19 1994 Analysis of a subdomain-based error estimator for finite element approximations of elliptic problems. Zbl 1049.65123Prudhomme, S.; Nobile, F.; Chamoin, L.; Oden, J. T. 19 2004 Implementation of an adaptive refinement technique for the SUPG algorithm. Zbl 0596.73066Devloo, Philippe; Oden, J. T.; Strouboulis, T. 19 1987 A posteriori error estimation of finite element approximations in fluid mechanics. Zbl 0711.76061Strouboulis, T.; Oden, J. T. 19 1990 Computable error estimators and adaptive techniques for fluid flow problems. Zbl 1141.76427Prudhomme, Serge; Oden, J. Tinsley 19 2003 Practical methods for a posteriori error estimation in engineering applications. Zbl 1038.74045Prudhomme, Serge; Oden, J. Tinsley; Westermann, Tim; Bass, Jon; Botkin, Mark E. 19 2003 Toward predictive multiscale modeling of vascular tumor growth, computational and experimental oncology for tumor prediction. Zbl 1360.92059Oden, J. Tinsley; Lima, Ernesto A. B. F.; Almeida, Regina C.; Feng, Yusheng; Rylander, Marissa Nichole; Fuentes, David; Faghihi, Danial; Rahman, Mohammad M.; DeWitt, Matthew; Gadde, Manasa; Zhou, J. Cliff 19 2016 A priori error estimations of \(hp\)-finite element approximations for hierarchical models of plate- and shell-like structures. Zbl 0884.73063Cho, J. R.; Oden, J. Tinsley 18 1996 A numerical analysis of a class of problems in elastodynamics with friction. Zbl 0527.73079Martins, J. A. C.; Oden, J. T. 18 1983 A priori modeling error estimates of hierarchical models for elasticity problems for plate- and shell-like structures. Zbl 0854.73082Cho, J. R.; Oden, J. T. 18 1996 An \(h\)-\(p\) Taylor-Galerkin finite element method for compressible Euler equations. Zbl 0745.76036Demkowicz, L.; Oden, J. Tinsley; Rachowicz, W.; Hardy, O. 18 1991 Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network. Zbl 1480.92046Fritz, Marvin; Jha, Prashant K.; Köppl, Tobias; Oden, J. Tinsley; Wohlmuth, Barbara 2 2021 Modeling and simulation of vascular tumors embedded in evolving capillary networks. Zbl 07415267Fritz, Marvin; Jha, Prashant K.; Köppl, Tobias; Oden, J. Tinsley; Wagner, Andreas; Wohlmuth, Barbara 1 2021 Bayesian-based predictions of COVID-19 evolution in Texas using multispecies mixture-theoretic continuum models. Zbl 1469.92111Jha, Prashant K.; Cao, Lianghao; Oden, J. Tinsley 7 2020 A coupled mass transport and deformation theory of multi-constituent tumor growth. Zbl 1477.74032Faghihi, Danial; Feng, Xinzeng; Lima, Ernesto A. B. F.; Oden, J. Tinsley; Yankeelov, Thomas E. 3 2020 A statistical framework for generating microstructures of two-phase random materials: application to fatigue analysis. Zbl 1435.82032Khristenko, Ustim; Constantinescu, Andrei; Tallec, Patrick Le; Oden, J. Tinsley; Wohlmuth, Barbara 2 2020 Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation. Zbl 1425.35075Fritz, Marvin; Lima, Ernesto A. B. F.; Nikolić, Vanja; Oden, J. Tinsley; Wohlmuth, Barbara 11 2019 On the unsteady Darcy-Forchheimer-Brinkman equation in local and nonlocal tumor growth models. Zbl 1425.35076Fritz, Marvin; Lima, Ernesto A. B. F.; Tinsley Oden, J.; Wohlmuth, Barbara 11 2019 Adaptive multiscale predictive modelling. Zbl 1430.60006Oden, J. Tinsley 14 2018 A hybrid three-scale model of tumor growth. Zbl 1381.92051Rocha, H. L.; Almeida, R. C.; Lima, E. A. B. F.; Resende, A. C. M.; Oden, J. T.; Yankeelov, T. E. 9 2018 Applied functional analysis. 3rd edition. Zbl 1379.46001Oden, John Tinsley; Demkowicz, Leszek F. 3 2018 Selection and validation of predictive models of radiation effects on tumor growth based on noninvasive imaging data. Zbl 1439.92110Lima, E. A. B. F.; Oden, J. T.; Wohlmuth, B.; Shahmoradi, A.; Hormuth, D. A.; Yankeelov, T. E.; Scarabosio, L.; Horger, T. 17 2017 Adaptive selection and validation of models of complex systems in the presence of uncertainty. Zbl 1377.92036Farrell-Maupin, Kathryn; Oden, J. T. 4 2017 A fully coupled space-time multiscale modeling framework for predicting tumor growth. Zbl 1439.74209Rahman, Mohammad Mamunur; Feng, Yusheng; Yankeelov, Thomas E.; Oden, J. Tinsley 2 2017 Selection, calibration, and validation of models of tumor growth. Zbl 1349.92075Lima, E. A. B. F.; Oden, J. T.; Hormuth, D. A. II; Yankeelov, T. E.; Almeida, R. C. 22 2016 Toward predictive multiscale modeling of vascular tumor growth, computational and experimental oncology for tumor prediction. Zbl 1360.92059Oden, J. Tinsley; Lima, Ernesto A. B. F.; Almeida, Regina C.; Feng, Yusheng; Rylander, Marissa Nichole; Fuentes, David; Faghihi, Danial; Rahman, Mohammad M.; DeWitt, Matthew; Gadde, Manasa; Zhou, J. Cliff 19 2016 A Bayesian framework for adaptive selection, calibration, and validation of coarse-grained models of atomistic systems. Zbl 1349.62078Farrell, Kathryn; Oden, J. Tinsley; Faghihi, Danial 12 2015 Analysis and numerical solution of stochastic phase-field models of tumor growth. Zbl 1326.92041Lima, Ernesto A. B. F.; Almeida, Regina C.; Oden, J. Tinsley 7 2015 A computational framework for dynamic data-driven material damage control, based on Bayesian inference and model selection. Zbl 1352.74275Prudencio, E. E.; Bauman, P. T.; Faghihi, D.; Ravi-Chandar, K.; Oden, J. T. 5 2015 A hybrid ten-species phase-field model of tumor growth. Zbl 1404.35459Lima, E. A. B. F.; Oden, J. T.; Almeida, R. C. 25 2014 Calibration and validation of coarse-grained models of atomic systems: application to semiconductor manufacturing. Zbl 1398.74487Farrell, Kathryn; Oden, J. Tinsley 4 2014 Bayesian calibration, validation, and uncertainty quantification of diffuse interface models of tumor growth. Zbl 1280.35163Hawkins-Daarud, Andrea; Prudhomme, Serge; van der Zee, Kristoffer G.; Oden, J. Tinsley 35 2013 Selection and assessment of phenomenological models of tumor growth. Zbl 1301.92034Oden, J. Tinsley; Prudencio, Ernesto E.; Hawkins-Daarud, Andrea 33 2013 Virtual model validation of complex multiscale systems: applications to nonlinear elastostatics. Zbl 1286.62016Oden, J. Tinsley; Prudencio, Ernesto E.; Bauman, Paul T. 2 2013 Numerical simulation of a thermodynamically consistent four-species tumor growth model. Zbl 1242.92030Hawkins-Daarud, Andrea; van der Zee, Kristoffer G.; Oden, J. Tinsley 81 2012 Analysis of an averaging operator for atomic-to-continuum coupling methods by the Arlequin approach. Zbl 1364.74093Prudhomme, Serge; Bouclier, Robin; Chamoin, Ludovic; Ben Dhia, Hachmi; Oden, J. Tinsley 3 2012 Goal-oriented error estimation for Cahn–Hilliard models of binary phase transition. Zbl 1428.35398van der Zee, Kristoffer G.; Oden, J. Tinsley; Prudhomme, Serge; Hawkins-Daarud, Andrea 15 2011 Control of modeling error in calibration and validation processes for predictive stochastic models. Zbl 1242.74232Oden, J. Tinsley; Prudhomme, Serge 4 2011 An introduction to mathematical modeling. A course in mechanics. Zbl 1251.81001Oden, J. Tinsley 4 2011 A new adaptive modeling strategy based on optimal control for atomic-to-continuum coupling simulations. Zbl 1230.74220Ben Dhia, H.; Chamoin, Ludovic; Oden, J. Tinsley; Prudhomme, Serge 3 2011 An introduction to mathematical modeling. A course in mechanics. Zbl 1227.00037Oden, John Tinsley 1 2011 General diffuse-interface theories and an approach to predictive tumor growth modeling. Zbl 1186.92024Oden, J. Tinsley; Hawkins, Andrea; Prudhomme, Serge 96 2010 Applied functional analysis. 2nd ed. Zbl 1200.46001Oden, J. Tinsley; Demkowicz, Leszek F. 17 2010 Solution verification, goal-oriented adaptive methods for stochastic advection-diffusion problems. Zbl 1231.76239Almeida, Regina C.; Oden, J. Tinsley 13 2010 Ghost forces and spurious effects in atomic-to-continuum coupling methods by the Arlequin approach. Zbl 1197.74004Chamoin, Ludovic; Prudhomme, Serge; Ben Dhia, H.; Oden, Tinsley 11 2010 Estimation and control of modeling error: a general approach to multiscale modeling. Zbl 1221.82012Oden, J. T.; Prudhomme, S.; Bauman, P. T.; Chamoin, L. 3 2010 Adaptive multiscale modeling of polymeric materials with Arlequin coupling and goals algorithms. Zbl 1229.74006Bauman, Paul T.; Oden, J. Tinsley; Prudhomme, Serge 31 2009 On the application of the Arlequin method to the coupling of particle and continuum models. Zbl 1252.74055Bauman, Paul T.; Ben Dhia, Hachmi; Elkhodja, Nadia; Oden, J. Tinsley; Prudhomme, Serge 51 2008 Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method. Zbl 1159.74303Prudhomme, S.; Ben Dhia, H.; Bauman, P. T.; Elkhodja, N.; Oden, J. T. 34 2008 A stochastic coupling method for atomic-to-continuum MonteCarlo simulations. Zbl 1194.74548Chamoin, Ludovic; Oden, J. T.; Prudhomme, Serge 12 2008 Dynamic data-driven finite element models for laser treatment of cancer. Zbl 1114.92043Oden, J. T.; Diller, K. R.; Bajaj, C.; Browne, J. C.; Hazle, J.; Babuška, I.; Bass, J.; Biduat, L.; Demkowicz, L.; Elliott, A.; Feng, Y.; Fuentes, D.; Prudhomme, S.; Rylander, M. N.; Stafford, R. J.; Zhang, Y. 4 2007 Multiscale modeling of physical phenomena: adaptive control of models. Zbl 1126.74006Oden, J. Tinsley; Prudhomme, Serge; Romkes, Albert; Bauman, Paul T. 54 2006 Extensions of goal-oriented error estimation methods to simulations of highly-nonlinear response of shock-loaded elastomer-reinforced structures. Zbl 1124.74047Fuentes, David; Littlefield, David; Oden, J. Tinsley; Prudhomme, Serge 8 2006 Finite elements of nonlinear continua. Reprint of the 1972 original ed. Zbl 1207.74125Oden, John Tinsley 7 2006 Convergence analysis of a discontinuous finite element formulation based on second-order derivatives. Zbl 1125.65097Romkes, Albert; Prudhomme, Serge; Oden, J. Tinsley 3 2006 The reliability of computer predictions: can they be trusted? Zbl 1096.65043Babuška, Ivo; Oden, J. Tinsley 2 2006 Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty. Zbl 1143.74373Oden, J. Tinsley; Babuška, Ivo; Nobile, Fabio; Feng, Yusheng; Tempone, Raul 17 2005 A posteriori error estimation for acoustic wave propagation problems. Zbl 1145.76033Oden, J. Tinsley; Prudhomme, Serge; Demkowicz, Leszek 16 2005 On the extension of goal-oriented error estimation and hierarchical modeling to discrete lattice models. Zbl 1098.82025Oden, J. T.; Prudhomme, S.; Bauman, P. 4 2005 Mathematical perspectives on large eddy simulation models for turbulent flows. Zbl 1094.76030Guermond, J.-L.; Oden, J. T.; Prudhomme, S. 45 2004 Verification and validation in computational engineering and science: basic concepts. Zbl 1198.74126Babuska, Ivo; Oden, J. Tinsley 31 2004 Analysis of a subdomain-based error estimator for finite element approximations of elliptic problems. Zbl 1049.65123Prudhomme, S.; Nobile, F.; Chamoin, L.; Oden, J. T. 19 2004 Adaptive modeling of wave propagation in heterogeneous elastic solids. Zbl 1133.74314Romkes, Albert; Oden, J. T. 6 2004 An interpretation of the Navier-Stokes-alpha model as a frame-indifferent Leray regularization. Zbl 1082.35120Guermond, J. L.; Oden, J. T.; Prudhomme, S. 28 2003 Research directions in computational mechanics. Zbl 1025.74503Oden, J. Tinsley; Belytschko, Ted; Babuska, Ivo; Hughes, T. J. R. 24 2003 A priori error analyses of a stabilized discontinuous Galerkin method. Zbl 1058.65122Romkes, A.; Prudhomme, S.; Oden, J. T. 23 2003 Computable error estimators and adaptive techniques for fluid flow problems. Zbl 1141.76427Prudhomme, Serge; Oden, J. Tinsley 19 2003 Practical methods for a posteriori error estimation in engineering applications. Zbl 1038.74045Prudhomme, Serge; Oden, J. Tinsley; Westermann, Tim; Bass, Jon; Botkin, Mark E. 19 2003 Error estimation of eigenfrequencies for elasticity and shell problems. Zbl 1058.74081Oden, J. Tinsley; Prudhomme, Serge; Westermann, Tim; Bass, Jon; Botkin, Mark E. 8 2003 A posteriori error estimation for a new stabilized discontinuous Galerkin method. Zbl 1046.65089Romkes, A.; Prudhomme, S.; Oden, J. T. 4 2003 Estimation of modeling error in computational mechanics. Zbl 1053.74049Oden, J. Tinsley; Prudhomme, Serge 74 2002 Numerical stability and error analysis for the incompressible Navier-Stokes equations. Zbl 1021.76029Prudhomme, S.; Oden, J. T. 5 2002 Additive Schwarz algorithms for solving \(hp\)-version finite element systems on triangular meshes. Zbl 1018.65126Korneev, V.; Flaherty, J. E.; Oden, J. T.; Fish, J. 1 2002 \(hp\)-version additive Schwarz algorithms on triangular meshes. Zbl 1038.65134Korneev, V.; Flaherty, J. E.; Oden, T.; Fish, J. 1 2002 Solution of stochastic partial differential equations using Galerkin finite element techniques. Zbl 1075.65006Deb, Manas K.; Babuška, Ivo M.; Oden, J. Tinsley 158 2001 Goal-oriented error estimation and adaptivity for the finite element method. Zbl 0987.65110Oden, J. T.; Prudhomme, S. 140 2001 Estimation of local model error and goal-oriented adaptive modeling of heterogeneous materials. II: A computational environment for adaptive modeling of heterogeneous elastic solids. Zbl 1030.74051Vemaganti, Kumar S.; Oden, J. Tinsley 40 2001 A priori error estimate for the Baumann-Oden version of the discontinuous Galerkin method. Zbl 1007.65084Prudhomme, Serge; Pascal, Frédéric; Oden, J. Tinsley; Romkes, Albert 29 2001 Modeling error and adapticity in nonlinear continuum mechanics. Zbl 1012.74081Oden, J. Tinsley; Prudhomme, Serge; Hammerand, Daniel C.; Kuczma, Mieczyslaw S. 16 2001 A posteriori error estimation in finite element analysis. Zbl 1008.65076Ainsworth, Mark; Oden, J. Tinsley 738 2000 Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. I: Error estimates and adaptive algorithms. Zbl 0992.74072Oden, J. Tinsley; Vemaganti, Kumar S. 102 2000 An adaptive-order discontinuous Galerkin method for the solution of the Euler equations of gas dynamics. Zbl 0984.76040Baumann, Carlos Erik; Oden, J. Tinsley 11 2000 Functionally graded material: A parametric study on thermal-stress characteristics using the Crank-Nicolson-Galerkin scheme. Zbl 0976.74064Cho, J. R.; Oden, J. Tinsley 10 2000 A conservative DGM for convection-diffusion and Navier-Stokes problems. Zbl 0988.76053Oden, J. Tinsley; Baumann, Carlos Erik 4 2000 A discontinuous \(hp\) finite element method for convection-diffusion problems. Zbl 0924.76051Baumann, Carlos Erik; Oden, J. Tinsley 212 1999 On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors. Zbl 0945.65123Prudhomme, S.; Oden, J. T. 144 1999 A discontinuous \(hp\) finite element method for the Euler and Navier-Stokes equations. Zbl 0985.76048Baumann, Carlos Erik; Oden, J. Tinsley 110 1999 A discontinuous \(hp\) finite element method for diffusion problems: 1-D analysis. Zbl 0940.65076Babuška, I.; Baumann, C. E.; Oden, J. T. 48 1999 Hierarchical modeling of heterogeneous solids. Zbl 0972.74014Oden, J. Tinsley; Vemaganti, Kumar; Moës, Nicolas 40 1999 A posteriori error estimation and error control for finite element approximations of the time-dependent Navier–Stokes equations. Zbl 0965.76046Prudhomme, S.; Oden, J. T. 16 1999 New approaches to error estimation and adaptivity for the Stokes and Oseen equations. Zbl 0984.76052Oden, J. T.; Prudhomme, S. 8 1999 Adaptive hierarchical modeling of heterogeneous structures. Zbl 1194.74031Oden, J. Tinsley; Vemaganti, Kumar 6 1999 Simplified methods and a posteriori error estimation for the homogenization of representative volume elements (RVE). Zbl 0982.74069Moës, Nicolas; Oden, J. Tinsley; Vemaganti, Kumar; Remacle, Jean-François 5 1999 A discontinuous \(hp\) finite element method for diffusion problems. Zbl 0926.65109Oden, J. Tinsley; Babuška, Ivo; Baumann, Carlos Erik 205 1998 A new cloud-based \(hp\) finite element method. Zbl 0956.74062Oden, J. T.; Duarte, C. A. M.; Zienkiewicz, O. C. 160 1998 Investigation of the interactions between the numerical and the modeling errors in the homogenized Dirichlet projection method. Zbl 0952.74072Moës, Nicolas; Oden, J. Tinsley; Zohdi, Tarek I. 5 1998 Advances in adaptive computational methods in mechanics. 3rd workshop, Cachan, France, September 17–19, 1997. Zbl 0915.76001 3 1998 Local and pollution error estimation for Stokesian flows. Zbl 0906.76038Oden, J. Tinsley; Feng, Yusheng; Prudhomme, Serge 1 1998 A posteriori error estimation in finite element analysis. Zbl 0895.76040Ainsworth, Mark; Oden, J. Tinsley 241 1997 A posteriori error estimators for the Stokes and Oseen equations. Zbl 0879.65067Ainsworth, Mark; Oden, J. Tinsley 56 1997 Analysis and adaptive modeling of highly heterogeneous elastic structures. Zbl 0924.73015Oden, J. Tinsley; Zohdi, Tarek I. 41 1997 Clouds, cracks and FEM’s. Zbl 0976.74071Oden, J. T.; Duarte, C. A. 30 1997 Parallel domain decomposition solver for adaptive \(hp\) finite element methods. Zbl 0890.65124Oden, J. T.; Patra, Abani; Feng, Yusheng 21 1997 Locking and boundary layer in hierarchical models for thin elastic structures. Zbl 0918.73130Cho, Jin-Rae; Oden, J. Tinsley 16 1997 A parallel multifrontal algorithm and its implementation. Zbl 0925.65077Geng, P.; Oden, J. T.; van de Geijn, R. A. 12 1997 Solution of singular problems using \(hp\) clouds. Zbl 0891.73067Oden, J. Tinsley; Duarte, C. Armando 11 1997 Computational techniques for adaptive \(hp\) finite element methods. Zbl 0897.65068Patra, Abani; Oden, J. Tinsley 4 1997 A posteriori error estimator and adaptive procedures for computation of shakedown and limit loads on pressure vessels. Zbl 0914.73057Franco, Jose Ricardo Queiroz; Oden, J. Tinsley; Ponter, Alan R. S.; Barros, Felicio B. 2 1997 An \(h\)-\(p\) adaptive method using clouds. Zbl 0918.73328Duarte, C. Armando; Oden, J. Tinsley 304 1996 \(H\)-\(p\) clouds – an \(h\)-\(p\) meshless method. Zbl 0869.65069Duarte, C. Armando; Oden, J. Tinsley 201 1996 \(hp\)-version discontinuous Galerkin methods for hyperbolic conservation laws. Zbl 0894.76036Bey, Kim S.; Oden, J. Tinsley 56 1996 ...and 201 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 6,765 Authors 148 Oden, John Tinsley 73 Sofonea, Mircea 66 Demkowicz, Leszek F. 65 Noor, Muhammad Aslam 56 Babuška, Ivo 48 Han, Weimin 37 Shillor, Meir 36 Belytschko, Ted Bohdan 35 Carey, Graham Francis 34 Hughes, Thomas J. R. 33 Prudhomme, Serge 32 Ladevèze, Pierre 30 Díez, Pedro 30 Migórski, Stanisław 29 Carstensen, Carsten 29 Strouboulis, Theofanis 28 Wheeler, Mary Fanett 28 Wohlmuth, Barbara I. 28 Wriggers, Peter 25 Ainsworth, Mark 25 Liu, Wing Kam 25 Yang, Yidu 24 Baccouch, Mahboub 24 Hild, Patrick 24 Rachowicz, Waldemar 23 Bordas, Stéphane Pierre Alain 22 Adjerid, Slimane 22 Huerta, Antonio 22 Li, Jichun 22 Li, Xiaolin 21 Chamoin, Ludovic 21 Duarte, Carlos Armando 21 Fernández, Jose Ramon 21 Nicaise, Serge 20 Karniadakis, George Em 20 Pardo, David 20 Repin, Sergeĭ Igorevich 20 Zhang, Zhimin 19 Chen, Jiun-Shyan 19 Loula, Abimael Fernando Dourado 19 Praetorius, Dirk 18 Barboteu, Mikaël 18 Liu, Gui-Rong 18 Reddy, Junuthula Narasimha 17 Bi, Hai 17 Fish, Jacob 17 Li, Zi-Cai 17 Sluys, Lambertus Johannes 16 Abdulle, Assyr 16 Flaherty, Joseph E. 16 Rocca, Elisabetta 16 Steinmann, Paul 16 Wick, Thomas 15 Calo, Victor Manuel 15 Feistauer, Miloslav 15 Garcke, Harald 15 Kikuchi, Noboru 15 Kuttler, Kenneth L. jun. 15 Lam, Kei Fong 15 Moës, Nicolas 15 Nouy, Anthony 15 Renard, Yves 15 Shephard, Mark S. 15 Tamma, Kumar K. 15 van der Zee, Kristoffer George 15 Wang, Fei 15 Zienkiewicz, Olgierd Cecil 14 Almeida, Regina C. 14 Cheng, Xiaoliang 14 Dumbser, Michael 14 Gudi, Thirupathi 14 Huang, Yunqing 14 Otárola, Enrique 14 Parés, Núria 14 Paszyński, Maciej 14 Sun, Shuyu 14 Vohralík, Martin 13 Baker, Allen J. 13 Banerjee, Uday 13 Dehghan Takht Fooladi, Mehdi 13 Dolejší, Vít 13 Ern, Alexandre 13 Giani, Stefano 13 Oh, Hae-Soo 13 Rank, Ernst 13 Reddy, B. Dayanand 13 Schroder, Andreas 13 Stein, Erwin 13 Werschulz, Arthur G. 12 Antonietti, Paola Francesca 12 Argyris, John Hadji 12 Barros, Felício Bruzzi 12 Chen, Yanping 12 Dawson, Clint N. 12 Devloo, Philippe Remy Bernard 12 Dhia, Hachmi Ben 12 Dostál, Zdeněk 12 Gatica, Gabriel N. 12 Gómez, Héctor J. 12 Haslinger, Jaroslav ...and 6,665 more Authors all top 5 Cited in 358 Serials 1,359 Computer Methods in Applied Mechanics and Engineering 340 International Journal for Numerical Methods in Engineering 259 Journal of Computational Physics 213 Computers & Mathematics with Applications 196 Computational Mechanics 183 Journal of Computational and Applied Mathematics 138 Applied Numerical Mathematics 135 Journal of Scientific Computing 120 Engineering Analysis with Boundary Elements 112 Numerische Mathematik 102 Applied Mathematics and Computation 79 Computers and Fluids 78 International Journal of Engineering Science 74 Mathematics of Computation 63 Journal of Mathematical Analysis and Applications 63 M\(^3\)AS. 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Modélisation Mathématique et Analyse Numérique 8 Journal of Complexity 8 Computational Optimization and Applications 8 Numerical Linear Algebra with Applications 8 International Journal of Numerical Analysis and Modeling 8 Discrete and Continuous Dynamical Systems. Series S 7 Soviet Applied Mechanics 7 Physica D 7 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 7 Foundations of Computational Mathematics 7 Acta Numerica 7 International Journal of Fracture 7 Journal of Theoretical Biology 7 Communications on Applied Mathematics and Computation 7 Fixed Point Theory and Algorithms for Sciences and Engineering 6 Journal of the Franklin Institute ...and 258 more Serials all top 5 Cited in 49 Fields 3,180 Numerical analysis (65-XX) 2,600 Mechanics of deformable solids (74-XX) 1,545 Partial differential equations (35-XX) 1,195 Fluid mechanics (76-XX) 575 Calculus of variations and optimal control; optimization (49-XX) 189 Biology and other natural sciences (92-XX) 135 Operator theory (47-XX) 117 Optics, electromagnetic theory (78-XX) 117 Classical thermodynamics, heat transfer (80-XX) 105 Probability theory and stochastic processes (60-XX) 91 Ordinary differential equations (34-XX) 80 Operations research, mathematical programming (90-XX) 78 Mechanics of particles and systems (70-XX) 77 Statistical mechanics, structure of matter (82-XX) 67 Statistics (62-XX) 62 Computer science (68-XX) 52 Geophysics (86-XX) 43 Systems theory; control (93-XX) 38 Approximations and expansions (41-XX) 34 Functional analysis (46-XX) 33 Global analysis, analysis on manifolds (58-XX) 29 Integral equations (45-XX) 27 Dynamical systems and ergodic theory (37-XX) 17 Potential theory (31-XX) 15 Real functions (26-XX) 15 Quantum theory (81-XX) 12 Information and communication theory, circuits (94-XX) 11 General and overarching topics; collections (00-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Differential geometry (53-XX) 7 Special functions (33-XX) 5 History and biography (01-XX) 5 Functions of a complex variable (30-XX) 4 Combinatorics (05-XX) 3 Measure and integration (28-XX) 2 Mathematical logic and foundations (03-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral transforms, operational calculus (44-XX) 2 Convex and discrete geometry (52-XX) 2 General topology (54-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Difference and functional equations (39-XX) 1 Algebraic topology (55-XX) 1 Relativity and gravitational theory (83-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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