Edit Profile (opens in new tab) Carstensen, Carsten Co-Author Distance Author ID: carstensen.carsten Published as: Carstensen, Carsten; Carstensen, C. Homepage: http://www2.mathematik.hu-berlin.de/~cc/cc_homepage/cc/education.shtml External Links: MGP · Google Scholar · ResearchGate · dblp · GND Documents Indexed: 295 Publications since 1987, including 1 Book and 6 Additional arXiv Preprints 14 Contributions as Editor Co-Authors: 140 Co-Authors with 267 Joint Publications 4,306 Co-Co-Authors all top 5 Co-Authors 42 single-authored 16 Funken, Stefan A. 14 Nataraj, Neela 13 Gallistl, Dietmar 12 Bartels, Sören 12 Gedicke, Joscha 11 Praetorius, Dirk 11 Stephan, Ernst Peter 9 Hoppe, Ronald H. W. 9 Hu, Jun 9 Merdon, Christian 9 Schedensack, Mira 9 Wriggers, Peter 8 Alberty, Jochen 8 Bringmann, Philipp 8 Rabus, Hella 7 Orlando, Antonio 7 Pani, Amiya Kumar 7 Petković, Miodrag S. 6 Dolzmann, Georg 6 Hackl, Klaus 6 Klose, Roland 6 Peterseim, Daniel 6 Plecháč, Petr 5 Hellwig, Friederike 5 Park, Eun-Jae 5 Puttkammer, Sophie 5 Weinberg, Kerstin 5 Zarrabi, Darius 4 Braess, Dietrich 4 Demkowicz, Leszek F. 4 Stein, Erwin 4 Tran, Ngoc Tien 3 Beckermann, Bernhard 3 Dond, Asha K. 3 Eigel, Martin 3 Gopalakrishnan, Jay 3 Gräßle, Benedikt 3 Hoppe, Ulrich 3 Köhler, Karoline 3 Prohl, Andreas 3 Reddy, B. Dayanand 3 Sauter, Stefan 3 Scherf, Oliver 3 Valdman, Jan 2 Allix, Olivier 2 Boiger, Wolfgang 2 Bösing, Paulo Rafael 2 Brenner, Susanne Cecelia 2 Brokate, Martin 2 Conti, Sergio 2 Ebobisse, François Bille 2 Engquist, Bjorn E. 2 Ern, Alexandre 2 Günther, David 2 Gwinner, Joachim 2 Hecht, Axel 2 Jansche, Stefan 2 Jensen, Max 2 Khot, Rekha 2 Liu, Dongjie 2 Liu, Steve Wenbin 2 Ma, Rui 2 Maischak, Matthias 2 Mallik, Gouranga 2 Mehrmann, Volker 2 Międlar, Agnieszka 2 Monk, Peter B. 2 Mühlbach, Günter W. 2 Schroder, Andreas 2 Schröder, Jörg 2 Shylaja, Devika 2 Steinmann, Paul 2 Thiele, Jan 2 Xie, Xiaoping 2 Yan, Ningning 2 Yu, Guozhu 1 Ainsworth, Mark 1 Altmann, Robert 1 Bahriawati, C. 1 Ball, John MacLeod 1 Bertrand, Fleurianne 1 Boffi, Daniele 1 Brink, Ulrich 1 Buffa, Annalisa 1 Carstensen, Christine 1 Causin, Paola 1 Dorfler, Willy 1 Estep, Donald J. 1 Faermann, Birgit 1 Feischl, Michael 1 Gaddam, Sharat 1 Gerritsma, Marc I. 1 Gudi, Thirupathi 1 Hackbusch, Wolfgang 1 Helm, D. S. 1 Heuer, Norbert 1 Huang, Yunqing 1 Huth, Robert 1 Jochimsen, K. 1 Kim, Dongho ...and 40 more Co-Authors all top 5 Serials 54 Numerische Mathematik 40 SIAM Journal on Numerical Analysis 19 Mathematics of Computation 18 Computer Methods in Applied Mechanics and Engineering 11 Computers & Mathematics with Applications 10 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 10 Oberwolfach Reports 9 IMA Journal of Numerical Analysis 9 Computational Methods in Applied Mathematics 7 SIAM Journal on Scientific Computing 6 Computing 6 Journal of Computational and Applied Mathematics 6 Journal of Computational Mathematics 6 PAMM. Proceedings in Applied Mathematics and Mechanics 5 International Journal for Numerical Methods in Engineering 5 Journal of Numerical Mathematics 4 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 4 Applied Numerical Mathematics 3 Mathematical Methods in the Applied Sciences 3 Computational Mechanics 3 Numerical Methods for Partial Differential Equations 3 Numerical Algorithms 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 BIT 2 Constructive Approximation 2 SIAM Journal on Mathematical Analysis 2 Numerical Mathematics: Theory, Methods and Applications 1 Applicable Analysis 1 Journal of the Australian Mathematical Society, Series B 1 Mathematische Semesterberichte 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal of Approximation Theory 1 Mathematische Nachrichten 1 Quarterly of Applied Mathematics 1 Computer Aided Geometric Design 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Facta Universitatis. Series Mathematics and Informatics 1 Journal of Scientific Computing 1 Journal of Integral Equations and Applications 1 International Journal of Computer Mathematics 1 Linear Algebra and its Applications 1 Serdica 1 Studia Universitatis Babeș-Bolyai. Mathematica 1 Continuum Mechanics and Thermodynamics 1 Communications in Numerical Methods in Engineering 1 Numerical Linear Algebra with Applications 1 East-West Journal of Numerical Mathematics 1 Advances in Computational Mathematics 1 Engineering Analysis with Boundary Elements 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Interfaces and Free Boundaries 1 International Journal of Numerical Analysis and Modeling 1 GAMM-Mitteilungen 1 CISM International Centre for Mechanical Sciences. Courses and Lectures 1 Lecture Notes in Computational Science and Engineering all top 5 Fields 255 Numerical analysis (65-XX) 114 Mechanics of deformable solids (74-XX) 108 Partial differential equations (35-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 22 Fluid mechanics (76-XX) 15 Functions of a complex variable (30-XX) 14 General and overarching topics; collections (00-XX) 12 Field theory and polynomials (12-XX) 10 Optics, electromagnetic theory (78-XX) 9 Real functions (26-XX) 7 Approximations and expansions (41-XX) 6 Potential theory (31-XX) 6 Integral equations (45-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Functional analysis (46-XX) 2 Mechanics of particles and systems (70-XX) 1 Number theory (11-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 262 Publications have been cited 4,290 times in 2,082 Documents Cited by ▼ Year ▼ A posteriori error estimate for the mixed finite element method. Zbl 0864.65068 Carstensen, Carsten 149 1997 Non-convex potentials and microstructures in finite-strain plasticity. Zbl 1008.74016 Carstensen, Carsten; Hackl, Klaus; Mielke, Alexander 139 2002 Axioms of adaptivity. Zbl 1350.65119 Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D. 135 2014 Breaking spaces and forms for the DPG method and applications including Maxwell equations. Zbl 1359.65249 Carstensen, C.; Demkowicz, L.; Gopalakrishnan, J. 94 2016 Edge residuals dominate a posteriori error estimates for low order finite element methods. Zbl 0938.65124 Carstensen, Carsten; Verfürth, Rüdiger 90 1999 Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. I: Low order conforming, nonconforming, and mixed FEM. Zbl 0997.65126 Carstensen, Carsten; Bartels, Sören 80 2002 Quasi-interpolation and a posteriori error analysis in finite element methods. Zbl 0948.65113 Carstensen, Carsten 72 1999 Remarks around 50 lines of Matlab: short finite element implementation. Zbl 0938.65129 Alberty, Jochen; Carstensen, Carsten; Funken, Stefan A. 70 1999 Three Matlab implementations of the lowest-order Raviart-Thomas MFEM with a posteriori error control. Zbl 1086.65107 Bahriawati, C.; Carstensen, C. 61 2005 A posteriori error estimates for mixed FEM in elasticity. Zbl 0928.74093 Carstensen, Carsten; Dolzmann, Georg 59 1998 A posteriori error estimates for nonconforming finite element methods. Zbl 1010.65044 Carstensen, Carsten; Bartels, Sören; Jansche, Stefan 59 2002 A posteriori error control for DPG methods. Zbl 1320.65171 Carstensen, Carsten; Demkowicz, Leszek; Gopalakrishnan, Jay 56 2014 A unifying theory of a posteriori error control for nonconforming finite element methods. Zbl 1127.65083 Carstensen, C.; Hu, Jun 55 2007 An a posteriori error estimate for a first-kind integral equation. Zbl 0854.65102 Carstensen, Carsten 54 1997 Guaranteed lower bounds for eigenvalues. Zbl 1320.65162 Carstensen, Carsten; Gedicke, Joscha 54 2014 A unifying theory of a posteriori finite element error control. Zbl 1100.65089 Carstensen, C. 50 2005 Guaranteed lower eigenvalue bounds for the biharmonic equation. Zbl 1298.65165 Carstensen, Carsten; Gallistl, Dietmar 49 2014 Averaging techniques yield reliable a posteriori finite element error control for obstacle problems. Zbl 1063.65050 Bartels, S.; Carstensen, C. 45 2004 Framework for the a posteriori error analysis of nonconforming finite elements. Zbl 1165.65072 Carstensen, Carsten; Hu, Jun; Orlando, Antonio 44 2007 Error reduction and convergence for an adaptive mixed finite element method. Zbl 1094.65112 Carstensen, Carsten; Hoppe, R. H. W. 43 2006 Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis. Zbl 1062.65113 Bartels, S.; Carstensen, C.; Dolzmann, G. 43 2004 Effective relaxation for microstructure simulations: algorithms and applications. Zbl 1112.74501 Bartels, S.; Carstensen, C.; Hackl, K.; Hoppe, U. 42 2004 Numerical solution of the scalar double-well problem allowing microstructure. Zbl 0870.65055 Carstensen, Carsten; Plechác, Petr 42 1997 Convergence analysis of an adaptive nonconforming finite element method. Zbl 1101.65102 Carstensen, Carsten; Hoppe, Ronald H. W. 41 2006 Fully reliable localized error control in the FEM. Zbl 0956.65099 Carstensen, Carsten; Funken, Stefan A. 40 2000 Constants in Clément-interpolation error and residual based a posteriori error estimates in finite element methods. Zbl 0973.65091 Carstensen, C.; Funken, S. A. 40 2000 Convergence analysis of a conforming adaptive finite element method for an obstacle problem. Zbl 1126.65058 Braess, Dietrich; Carstensen, Carsten; Hoppe, Ronald H. W. 39 2007 A posteriori error estimate and h-adaptive algorithm on surfaces from Symm’s integral equation. Zbl 1018.65138 Carstensen, C.; Maischak, M.; Stephan, E. P. 39 2001 A posteriori error estimates for boundary element methods. Zbl 0831.65120 Carstensen, Carsten; Stephan, Ernst P. 38 1995 Matlab implementation of the finite element method in elasticity. Zbl 1239.74092 Alberty, Jochen; Carstensen, Carsten; Funken, Stefan A.; Klose, Roland 37 2002 Weierstrass formula and zero-finding methods. Zbl 0821.65028 Petković, Miodrag S.; Carstensen, Carsten; Trajkovíc, Miroslav 35 1995 A priori and a posteriori pseudostress-velocity mixed finite element error analysis for the Stokes problem. Zbl 1232.65098 Carstensen, Carsten; Kim, Dongho; Park, Eun-Jae 35 2011 Adaptive numerical analysis in primal elastoplasticity with hardening. Zbl 0956.74049 Alberty, Jochen; Carstensen, Carsten; Zarrabi, Darius 33 1999 A posteriori error control in low-order finite element discretisations of incompressible stationary flow problems. Zbl 1014.76042 Carstensen, Carsten; Funken, Stefan A. 33 2001 Merging the Bramble-Pasciak-Steinbach and the Crouzeix-Thomée criterion for \(H^1\)-stability of the \(L^2\)-projection onto finite element spaces. Zbl 0989.65123 Carstensen, Carsten 33 2002 A review of unified a posteriori finite element error control. Zbl 1289.65249 Carstensen, C.; Eigel, M.; Hoppe, R. H. W.; Löbhard, C. 32 2012 A theory of discretization for nonlinear evolution inequalities applied to parabolic Signorini problems. Zbl 0954.65052 Carstensen, Carsten; Gwinner, Joachim 31 1999 Residual-based a posteriori error estimate for hypersingular equation on surfaces. Zbl 1063.65116 Carstensen, Carsten; Maischak, M.; Praetorius, D.; Stephan, E. P. 31 2004 An oscillation-free adaptive FEM for symmetric eigenvalue problems. Zbl 1227.65106 Carstensen, Carsten; Gedicke, Joscha 30 2011 Averaging technique for FE – a posteriori error control in elasticity. I: Conforming FEM. Zbl 0981.74063 Carstensen, Carsten; Funken, Stefan A. 30 2001 Explicit and averaging a posteriori error estimates for adaptive finite volume methods. Zbl 1084.65112 Carstensen, C.; Lazarov, R.; Tomov, S. 30 2005 Explicit error estimates for Courant, Crouzeix-Raviart and Raviart-Thomas finite element methods. Zbl 1274.65290 Carstensen, Carsten; Gedicke, Joscha; Rim, Donsub 30 2012 Axioms of adaptivity with separate marking for data resolution. Zbl 1377.65147 Carstensen, C.; Rabus, H. 29 2017 Local stress regularity in scalar nonconvex variational problems. Zbl 1012.49027 Carstensen, Carsten; Müller, Stefan 28 2002 Adaptive coupling of boundary elements and finite elements. Zbl 0849.65083 Carstensen, Carsten; Stephan, Ernst P. 26 1995 Adaptive boundary element methods for some first kind integral equations. Zbl 0863.65073 Carstensen, Carsten; Stephan, Ernst P. 26 1996 An adaptive finite element eigenvalue solver of asymptotic quasi-optimal computational complexity. Zbl 1254.65123 Carstensen, Carsten; Gedicke, Joscha 24 2012 A unifying theory of a posteriori error control for discontinuous Galerkin FEM. Zbl 1169.65106 Carstensen, Carsten; Gudi, Thirupathi; Jensen, Max 24 2009 Uniform convergence and a posteriori error estimators for the enhanced strain finite element method. Zbl 1050.65097 Braess, D.; Carstensen, C.; Reddy, B. D. 24 2004 All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable. Zbl 1067.65115 Carstensen, C. 24 2004 Averaging techniques for the effective numerical solution of Symm’s integral equation of the first kind. Zbl 1105.65124 Carstensen, Carsten; Praetorius, Dirk 24 2006 An adaptive mesh-refining algorithm allowing for an \(H^1\) stable \(L^2\) projection onto Courant finite element spaces. Zbl 1064.65143 Carstensen, Carsten 24 2004 On the adaptive coupling of FEM and BEM in 2-d elasticity. Zbl 0880.73062 Carstensen, C.; Funken, S. A.; Stephan, E. P. 24 1997 Some improved inclusion methods for polynomial roots with Weierstrass’ corrections. Zbl 0776.65036 Petković, Miodrag S.; Carstensen, Carsten 24 1993 Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems. Zbl 1311.65136 Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 24 2015 Comparison results of finite element methods for the Poisson model problem. Zbl 1261.65115 Carstensen, C.; Peterseim, D.; Schedensack, M. 24 2012 Numerical approximation of Young measures in non-convex variational problems. Zbl 0945.65070 Carstensen, Carsten; Roubíček, Tomáš 23 2000 Adaptive finite elements for elastic bodies in contact. Zbl 0940.74058 Carstensen, C.; Scherf, O.; Wriggers, P. 23 1999 Efficiency of a posteriori BEM-error estimates for first-kind integral equations on quasi-uniform meshes. Zbl 0849.65084 Carstensen, Carsten 22 1996 Locking-free adaptive mixed finite element methods in linear elasticity. Zbl 1004.74068 Carstensen, C.; Dolzmann, G.; Funken, S. A.; Helm, D. S. 22 2000 Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. II: Higher order FEM. Zbl 0997.65127 Bartels, Sören; Carstensen, Carsten 22 2002 The arnold-winther mixed FEM in linear elasticity. I: Implementation and numerical verification. Zbl 1194.74374 Carstensen, C.; Günther, D.; Reininghaus, J.; Thiele, J. 22 2008 Numerical analysis of the primal problem of elastoplasticity with hardening. Zbl 0947.74061 Carstensen, Carsten 21 1999 Computational competition of symmetric mixed FEM in linear elasticity. Zbl 1230.74172 Carstensen, C.; Eigel, M.; Gedicke, J. 21 2011 Convergence and optimality of adaptive least squares finite element methods. Zbl 1327.65212 Carstensen, Carsten; Park, Eun-Jae 21 2015 Optimal adaptive nonconforming FEM for the Stokes problem. Zbl 1316.76046 Carstensen, Carsten; Peterseim, Daniel; Rabus, Hella 21 2013 An optimal adaptive mixed finite element method. Zbl 1215.65173 Carstensen, Carsten; Rabus, Hella 20 2011 Some remarks on the history and future of averaging techniques in a posteriori finite element error analysis. Zbl 1073.65120 Carstensen, Carsten 20 2004 A discrete Helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes. Zbl 1362.65123 Carstensen, Carsten; Gallistl, Dietmar; Hu, Jun 20 2014 A posteriori finite element error control for the \(p\)-Laplace problem. Zbl 1050.65101 Carstensen, Carsten; Klose, R. 19 2003 Low-order discontinuous Petrov-Galerkin finite element methods for linear elasticity. Zbl 1457.65185 Carstensen, C.; Hellwig, F. 19 2016 Estimator competition for Poisson problems. Zbl 1224.65253 Carstensen, C.; Merdon, C. 18 2010 Fast parallel solvers for symmetric boundary element domain decomposition equations. Zbl 0907.65119 Carstensen, C.; Kuhn, M.; Langer, U. 18 1998 Mathematical foundation of a posteriori error estimates and adaptive mesh-refining algorithms for boundary integral equations of the first kind. Zbl 1007.65100 Carstensen, C.; Faermann, B. 18 2001 Adaptive finite element methods for microstructures? Numerical experiments for a 2-well benchmark. Zbl 1090.74054 Carstensen, C.; Jochimsen, K. 18 2003 A posteriori error estimators for convection-diffusion eigenvalue problems. Zbl 1295.65108 Gedicke, J.; Carstensen, C. 18 2014 Quasi-optimal adaptive pseudostress approximation of the Stokes equations. Zbl 1383.76333 Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 18 2013 Averaging techniques for the a posteriori BEM error control for a hypersingular integral equation in two dimensions. Zbl 1140.65089 Carstensen, Carsten; Praetorius, Dirk 17 2007 Hanging nodes in the unifying theory of a posteriori finite element error control. Zbl 1212.65423 Carstensen, C.; Hu, Jun 17 2009 Elastoviscoplastic finite element analysis in 100 lines of Matlab. Zbl 1099.74544 Carstensen, C.; Klose, R. 17 2002 Medius analysis and comparison results for first-order finite element methods in linear elasticity. Zbl 1329.74272 Carstensen, C.; Schedensack, M. 17 2015 A priori and a posteriori error control of discontinuous Galerkin finite element methods for the von Kármán equations. Zbl 1465.65129 Carstensen, Carsten; Mallik, Gouranga; Nataraj, Neela 17 2019 Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem. Zbl 1285.65079 Carstensen, C.; Merdon, C. 17 2013 Convergence analysis of an adaptive edge finite element method for the 2D eddy current equations. Zbl 1073.78008 Carstensen, C.; Hoppe, R. H. W. 16 2005 On quadratic-like convergence of the means for two methods for simultaneous rootfinding of polynomials. Zbl 0779.65030 Carstensen, Carsten 16 1993 Interface problem in holonomic elastoplasticity. Zbl 0792.73017 Carstensen, Carsten 16 1993 Low-order dPG-FEM for an elliptic PDE. Zbl 1364.65242 Carstensen, C.; Gallistl, D.; Hellwig, F.; Weggler, L. 16 2014 Numerical analysis of compatible phase transitions in elastic solids. Zbl 1049.74062 Carstensen, Carsten; Plechác, Petr 15 2000 Numerical analysis of a relaxed variational model of hysteresis in two-phase solids. Zbl 1007.74062 Carstensen, Carsten; Plecháč, Petr 15 2001 An a priori error estimate for finite element discretizations in nonlinear elasticity for polyconvex materials under small loads. Zbl 1057.74038 Carstensen, Carsten; Dolzmann, Georg 15 2004 Symmetric coupling of boundary elements and Raviart-Thomas-type mixed finite elements in elastostatics. Zbl 0877.73063 Brink, Ulrich; Carstensen, Carsten; Stein, Erwin 15 1996 How to prove the discrete reliability for nonconforming finite element methods. Zbl 1463.65362 Carstensen, Carsten; Puttkammer, Sophie 15 2020 An adaptive homotopy approach for non-selfadjoint eigenvalue problems. Zbl 1263.65106 Carstensen, Carsten; Gedicke, Joscha; Mehrmann, Volker; Miedlar, Agnieszka 14 2011 A posteriori FE error control for \(p\)-Laplacian by gradient recovery in quasi-norm. Zbl 1121.65111 Carstensen, Carsten; Liu, W.; Yan, N. 14 2006 FEM and BEM coupling for a nonlinear transmission problem with Signorini contact. Zbl 0896.65079 Carstensen, Carsten; Gwinner, Joachim 14 1997 Mixed analytical-numerical relaxation in finite single-slip crystal plasticity. Zbl 1160.74326 Carstensen, Carsten; Conti, Sergio; Orlando, Antonio 14 2008 A posteriori error estimate for the symmetric coupling of finite elements and boundary elements. Zbl 0863.65070 Carstensen, C. 14 1996 Nonconforming FEMs for an optimal design problem. Zbl 1312.74036 Carstensen, C.; Liu, D. J. 14 2015 Constants in discrete Poincaré and Friedrichs inequalities and discrete quasi-interpolation. Zbl 1401.65130 Carstensen, Carsten; Hellwig, Friederike 14 2018 Adaptive techniques for the contact of elastic bodies. Zbl 1122.74528 Wriggers, P.; Scherf, O.; Carstensen, C. 13 1994 Direct guaranteed lower eigenvalue bounds with optimal a priori convergence rates for the bi-Laplacian. Zbl 1521.65118 Carstensen, Carsten; Puttkammer, Sophie 3 2023 Nonconforming virtual elements for the biharmonic equation with Morley degrees of freedom on polygonal meshes. Zbl 1528.65103 Carstensen, Carsten; Khot, Rekha; Pani, Amiya K. 1 2023 Stabilization-free HHO a posteriori error control. Zbl 07732060 Bertrand, Fleurianne; Carstensen, Carsten; Gräßle, Benedikt; Ngoc Tien Tran 1 2023 Lowest-order equivalent nonstandard finite element methods for biharmonic plates. Zbl 1483.65177 Carstensen, Carsten; Nataraj, Neela 5 2022 A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems. Zbl 1496.65209 Carstensen, Carsten; Khot, Rekha; Pani, Amiya K. 4 2022 Critical functions and inf-sup stability of Crouzeix-Raviart elements. Zbl 1524.65773 Carstensen, C.; Sauter, S. 4 2022 Crouzeix-Raviart triangular elements are inf-sup stable. Zbl 1496.65211 Carstensen, Carsten; Sauter, Stefan A. 3 2022 Stability of mixed FEMs for non-selfadjoint indefinite second-order linear elliptic PDEs. Zbl 1491.65128 Carstensen, C.; Nataraj, Neela; Pani, Amiya K. 2 2022 Adaptive least-squares, discontinuous Petrov-Galerkin, and hybrid high-order methods. Zbl 1513.74150 Bringmann, Philipp; Carstensen, Carsten; Tran, Ngoc Tien 1 2022 Nonconforming finite element discretization for semilinear problems with trilinear nonlinearity. Zbl 1460.65145 Carstensen, Carsten; Mallik, Gouranga; Nataraj, Neela 10 2021 A priori and a posteriori error analysis of the Crouzeix-Raviart and Morley FEM with original and modified right-hand sides. Zbl 1476.65294 Carstensen, Carsten; Nataraj, Neela 8 2021 Adaptive Morley FEM for the von Kármán equations with optimal convergence rates. Zbl 1467.65107 Carstensen, Carsten; Nataraj, Neela 6 2021 Hierarchical Argyris finite element method for adaptive and multigrid algorithms. Zbl 1473.65291 Carstensen, Carsten; Hu, Jun 3 2021 Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method. Zbl 1502.65179 Carstensen, Carsten; Ern, Alexandre; Puttkammer, Sophie 3 2021 Unstabilized hybrid high-order method for a class of degenerate convex minimization problems. Zbl 1473.65292 Carstensen, Carsten; Tran, Tien 3 2021 Adaptive mixed finite element methods for non-self-adjoint indefinite second-order elliptic PDEs with optimal rates. Zbl 1468.65185 Carstensen, Carsten; Ma, Rui 2 2021 Collective marking for arbitrary order adaptive least-squares finite element methods with optimal rates. Zbl 1524.65772 Carstensen, Carsten; Ma, Rui 2 2021 Morley finite element method for the von Kármán obstacle problem. Zbl 07420191 Carstensen, Carsten; Gaddam, Sharat; Nataraj, Neela; Pani, Amiya K.; Shylaja, Devika 1 2021 How to prove the discrete reliability for nonconforming finite element methods. Zbl 1463.65362 Carstensen, Carsten; Puttkammer, Sophie 15 2020 Collective marking for adaptive least-squares finite element methods with optimal rates. Zbl 1426.65171 Carstensen, Carsten 7 2020 A skeletal finite element method can compute lower eigenvalue bounds. Zbl 1475.65178 Carstensen, Carsten; Zhai, Qilong; Zhang, Ran 5 2020 A priori and a posteriori error control of discontinuous Galerkin finite element methods for the von Kármán equations. Zbl 1465.65129 Carstensen, Carsten; Mallik, Gouranga; Nataraj, Neela 17 2019 Quasi-optimality of adaptive mixed FEMs for non-selfadjoint indefinite second-order linear elliptic problems. Zbl 1420.65108 Carstensen, Carsten; Dond, Asha K.; Rabus, Hella 6 2019 Residual-based a posteriori error analysis for symmetric mixed Arnold-Winther FEM. Zbl 1426.65162 Carstensen, Carsten; Gallistl, Dietmar; Gedicke, Joscha 5 2019 Convergence of \(\mathrm{dG}(1)\) in elastoplastic evolution. Zbl 1433.65283 Carstensen, Carsten; Liu, Dongjie; Alberty, Jochen 1 2019 Constants in discrete Poincaré and Friedrichs inequalities and discrete quasi-interpolation. Zbl 1401.65130 Carstensen, Carsten; Hellwig, Friederike 14 2018 Nonlinear discontinuous Petrov-Galerkin methods. Zbl 1398.65292 Carstensen, C.; Bringmann, P.; Hellwig, F.; Wriggers, P. 11 2018 An adaptive least-squares FEM for linear elasticity with optimal convergence rates. Zbl 1462.65179 Bringmann, P.; Carstensen, C.; Starke, Gerhard 10 2018 Asymptotic exactness of the least-squares finite element residual. Zbl 1397.65230 Carstensen, Carsten; Storn, Johannes 10 2018 Three first-order finite volume element methods for Stokes equations under minimal regularity assumptions. Zbl 1412.65181 Carstensen, Carsten; Dond, Asha K.; Nataraj, Neela; Pani, Amiya K. 8 2018 A low-order discontinuous Petrov-Galerkin method for the Stokes equations. Zbl 1401.65131 Carstensen, Carsten; Puttkammer, Sophie 7 2018 Optimal convergence rates for adaptive lowest-order discontinuous Petrov-Galerkin schemes. Zbl 1395.65140 Carstensen, Carsten; Hellwig, Friederike 5 2018 Axioms of adaptivity with separate marking for data resolution. Zbl 1377.65147 Carstensen, C.; Rabus, H. 29 2017 Convergence of natural adaptive least squares finite element methods. Zbl 1378.65176 Carstensen, Carsten; Park, Eun-Jae; Bringmann, Philipp 11 2017 Nonconforming FEM for the obstacle problem. Zbl 1433.65284 Carstensen, C.; Köhler, K. 9 2017 An adaptive least-squares FEM for the Stokes equations with optimal convergence rates. Zbl 1381.76156 Bringmann, P.; Carstensen, C. 8 2017 \(h\)-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates. Zbl 1402.65150 Bringmann, P.; Carstensen, C. 6 2017 Efficient discrete Lagrange multipliers in three first-order finite element discretizations for the a posteriori error control in an obstacle problem. Zbl 1359.65101 Carstensen, C.; Köhler, K. 2 2017 Flow relations and yield functions for dissipative strain-gradient plasticity. Zbl 1382.74023 Carstensen, Carsten; Ebobisse, François; McBride, Andrew T.; Reddy, B. Daya; Steinmann, Paul 1 2017 Breaking spaces and forms for the DPG method and applications including Maxwell equations. Zbl 1359.65249 Carstensen, C.; Demkowicz, L.; Gopalakrishnan, J. 94 2016 Low-order discontinuous Petrov-Galerkin finite element methods for linear elasticity. Zbl 1457.65185 Carstensen, C.; Hellwig, F. 19 2016 \(L^{2}\) best approximation of the elastic stress in the Arnold-Winther FEM. Zbl 1433.74102 Carstensen, C.; Gallistl, D.; Schedensack, M. 13 2016 Error analysis of nonconforming and mixed FEMs for second-order linear non-selfadjoint and indefinite elliptic problems. Zbl 1342.65214 Carstensen, Carsten; Dond, Asha K.; Nataraj, Neela; Pani, Amiya K. 11 2016 Comparison results and unified analysis for first-order finite volume element methods for a Poisson model problem. Zbl 1433.65254 Carstensen, Carsten; Nataraj, Neela; Pani, Amiya K. 11 2016 Justification of the saturation assumption. Zbl 1348.65161 Carstensen, C.; Gallistl, D.; Gedicke, J. 6 2016 The norm of a discretized gradient in \(H(\mathrm{div})^*\) for a posteriori finite element error analysis. Zbl 1352.65440 Carstensen, Carsten; Peterseim, Daniel; Schröder, Andreas 6 2016 Robust residual-based a posteriori Arnold-winther mixed finite element analysis in elasticity. Zbl 1425.74455 Carstensen, Carsten; Gedicke, Joscha 6 2016 A natural nonconforming FEM for the Bingham flow problem is quasi-optimal. Zbl 1457.65186 Carstensen, C.; Reddy, B. D.; Schedensack, M. 5 2016 Guaranteed velocity error control for the pseudostress approximation of the Stokes equations. Zbl 1401.76083 Bringmann, P.; Carstensen, C.; Merdon, C. 5 2016 Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems. Zbl 1311.65136 Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 24 2015 Convergence and optimality of adaptive least squares finite element methods. Zbl 1327.65212 Carstensen, Carsten; Park, Eun-Jae 21 2015 Medius analysis and comparison results for first-order finite element methods in linear elasticity. Zbl 1329.74272 Carstensen, C.; Schedensack, M. 17 2015 Nonconforming FEMs for an optimal design problem. Zbl 1312.74036 Carstensen, C.; Liu, D. J. 14 2015 Comparison results of nonstandard \(P_2\) finite element methods for the biharmonic problem. Zbl 1327.65211 Carstensen, Carsten; Gallistl, Dietmar; Nataraj, Neela 7 2015 Comparison results for the Stokes equations. Zbl 1320.76062 Carstensen, C.; Köhler, K.; Peterseim, D.; Schedensack, M. 5 2015 An optimal adaptive finite element method for an obstacle problem. Zbl 1317.65232 Carstensen, Carsten; Hu, Jun 5 2015 Discontinuous Galerkin with weakly over-penalized techniques for Reissner-Mindlin plates. Zbl 1329.74269 Bösing, Paulo Rafael; Carstensen, Carsten 4 2015 Weakly over-penalized discontinuous Galerkin schemes for Reissner-Mindlin plates without the shear variable. Zbl 1401.65128 Bösing, Paulo Rafael; Carstensen, Carsten 3 2015 Convergence of adaptive finite element methods for a nonconvex double-well minimization problem. Zbl 1329.74273 Carstensen, Carsten; Dolzmann, Georg 3 2015 Numerical algorithms for the simulation of finite plasticity with microstructures. Zbl 1371.74257 Carstensen, Carsten; Gallistl, Dietmar; Krämer, Boris 1 2015 Axioms of adaptivity. Zbl 1350.65119 Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D. 135 2014 A posteriori error control for DPG methods. Zbl 1320.65171 Carstensen, Carsten; Demkowicz, Leszek; Gopalakrishnan, Jay 56 2014 Guaranteed lower bounds for eigenvalues. Zbl 1320.65162 Carstensen, Carsten; Gedicke, Joscha 54 2014 Guaranteed lower eigenvalue bounds for the biharmonic equation. Zbl 1298.65165 Carstensen, Carsten; Gallistl, Dietmar 49 2014 A discrete Helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes. Zbl 1362.65123 Carstensen, Carsten; Gallistl, Dietmar; Hu, Jun 20 2014 A posteriori error estimators for convection-diffusion eigenvalue problems. Zbl 1295.65108 Gedicke, J.; Carstensen, C. 18 2014 Low-order dPG-FEM for an elliptic PDE. Zbl 1364.65242 Carstensen, C.; Gallistl, D.; Hellwig, F.; Weggler, L. 16 2014 Computational survey on a posteriori error estimators for the Crouzeix-Raviart nonconforming finite element method for the Stokes problem. Zbl 1285.65072 Carstensen, Carsten; Merdon, Christian 10 2014 An adaptive finite element method with asymptotic saturation for eigenvalue problems. Zbl 1306.65272 Carstensen, C.; Gedicke, J.; Mehrmann, V.; Miȩdlar, A. 3 2014 Refined fully explicit a posteriori residual-based error control. Zbl 1309.65124 Carstensen, C.; Merdon, C. 2 2014 Optimal adaptive nonconforming FEM for the Stokes problem. Zbl 1316.76046 Carstensen, Carsten; Peterseim, Daniel; Rabus, Hella 21 2013 Quasi-optimal adaptive pseudostress approximation of the Stokes equations. Zbl 1383.76333 Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 18 2013 Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem. Zbl 1285.65079 Carstensen, C.; Merdon, C. 17 2013 Discrete reliability for Crouzeix-Raviart FEMs. Zbl 1321.65171 Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 10 2013 A posteriori error estimates for nonconforming finite element methods for fourth-order problems on rectangles. Zbl 1316.74060 Carstensen, Carsten; Gallistl, Dietmar; Hu, Jun 9 2013 Effective postprocessing for equilibration a posteriori error estimators. Zbl 1267.65162 Carstensen, C.; Merdon, C. 9 2013 A posteriori error estimator competition for conforming obstacle problems. Zbl 1364.65243 Carstensen, C.; Merdon, C. 6 2013 Finite element network approximation of conductivity in particle composites. Zbl 1329.74284 Peterseim, Daniel; Carstensen, Carsten 3 2013 Aspects of guaranteed error control in CPDEs. Zbl 1275.65075 Carstensen, C.; Merdon, C.; Neumann, Johannes 1 2013 A review of unified a posteriori finite element error control. Zbl 1289.65249 Carstensen, C.; Eigel, M.; Hoppe, R. H. W.; Löbhard, C. 32 2012 Explicit error estimates for Courant, Crouzeix-Raviart and Raviart-Thomas finite element methods. Zbl 1274.65290 Carstensen, Carsten; Gedicke, Joscha; Rim, Donsub 30 2012 An adaptive finite element eigenvalue solver of asymptotic quasi-optimal computational complexity. Zbl 1254.65123 Carstensen, Carsten; Gedicke, Joscha 24 2012 Comparison results of finite element methods for the Poisson model problem. Zbl 1261.65115 Carstensen, C.; Peterseim, D.; Schedensack, M. 24 2012 The adaptive nonconforming FEM for the pure displacement problem in linear elasticity is optimal and robust. Zbl 1397.74183 Carstensen, Carsten; Rabus, Hella 11 2012 P\(_1\)-nonconforming finite elements on triangulations into triangles and quadrilaterals. Zbl 1251.65156 Altmann, Robert; Carstensen, Carsten 10 2012 Convergence of adaptive boundary element methods. Zbl 1238.65124 Carstensen, Carsten; Praetorius, Dirk 7 2012 Mixed finite element method for a degenerate convex variational problem from topology optimization. Zbl 1314.65088 Carstensen, Carsten; Günther, David; Rabus, Hella 5 2012 Numerical experiments for the Arnold-Einther mixed finite elements for the Stokes problem. Zbl 1250.76130 Carstensen, Carsten; Gedicke, Joscha; Park, Eun-Jae 5 2012 Stabilisation yields strong convergence of macroscopic magnetisation vectors for micromagnetics without exchange energy. Zbl 1247.78051 Carstensen, C.; Praetorius, D. 2 2012 A priori and a posteriori pseudostress-velocity mixed finite element error analysis for the Stokes problem. Zbl 1232.65098 Carstensen, Carsten; Kim, Dongho; Park, Eun-Jae 35 2011 An oscillation-free adaptive FEM for symmetric eigenvalue problems. Zbl 1227.65106 Carstensen, Carsten; Gedicke, Joscha 30 2011 Computational competition of symmetric mixed FEM in linear elasticity. Zbl 1230.74172 Carstensen, C.; Eigel, M.; Gedicke, J. 21 2011 An optimal adaptive mixed finite element method. Zbl 1215.65173 Carstensen, Carsten; Rabus, Hella 20 2011 An adaptive homotopy approach for non-selfadjoint eigenvalue problems. Zbl 1263.65106 Carstensen, Carsten; Gedicke, Joscha; Mehrmann, Volker; Miedlar, Agnieszka 14 2011 A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates. Zbl 1225.74081 Carstensen, Carsten; Xie, Xiaoping; Yu, Guozhu; Zhou, Tianxiao 11 2011 Uniform convergence and a posteriori error estimation for assumed stress hybrid finite element methods. Zbl 1230.74205 Yu, Guozhu; Xie, Xiaoping; Carstensen, Carsten 10 2011 An adaptive hybridized interior penalty discontinuous Galerkin method for H(curl)-elliptic problems. Zbl 1249.65228 Carstensen, C.; Hoppe, R. H. W.; Sharma, N.; Warburton, T. 8 2011 Remarks on the state of the art of a posteriori error control of elliptic PDEs in energy norms in practise. Zbl 1265.65225 Carstensen, Carsten; Merdon, Christian 1 2011 Estimator competition for Poisson problems. Zbl 1224.65253 Carstensen, C.; Merdon, C. 18 2010 Analysis of a class of penalty methods for computing singular minimizers. Zbl 1283.65097 Carstensen, C.; Ortner, C. 5 2010 ...and 162 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,147 Authors 146 Carstensen, Carsten 68 Praetorius, Dirk 45 Gatica, Gabriel N. 44 Petković, Miodrag S. 39 Stephan, Ernst Peter 34 Führer, Thomas 30 Hu, Jun 26 Demkowicz, Leszek F. 25 Vohralík, Martin 24 Heuer, Norbert 24 Mosler, Jörn 23 Park, Eun-Jae 22 Feischl, Michael 21 Ern, Alexandre 21 Yang, Yidu 20 Bartels, Sören 20 Karkulik, Michael 19 Gudi, Thirupathi 19 Hackl, Klaus 19 Nataraj, Neela 19 Valdman, Jan 17 Bertrand, Fleurianne 17 Mielke, Alexander 17 Repin, Sergeĭ Igorevich 16 Gallistl, Dietmar 16 Gedicke, Joscha 16 Huang, Yunqing 16 Peterseim, Daniel 16 Wohlmuth, Barbara I. 15 Funken, Stefan A. 15 Gantner, Gregor 15 Li, Jichun 15 Oyarzúa, Ricardo 15 Ruiz-Baier, Ricardo 15 Xie, Xiaoping 14 Dolzmann, Georg 14 Hoppe, Ronald H. W. 14 Melenk, Jens Markus 13 Bi, Hai 13 Conti, Sergio 13 Maischak, Matthias 13 Milošević, Dušan M. 13 Nicaise, Serge 13 Reddy, B. Dayanand 13 Roubíček, Tomáš 13 Zhao, Lina 12 Barrios, Tomás P. 12 Du, Shaohong 12 Merdon, Christian 12 Migórski, Stanisław 12 Schroder, Andreas 12 Stenberg, Rolf 12 Stevenson, Rob P. 11 Banz, Lothar 11 Boffi, Daniele 11 Han, Weimin 11 Hintermüller, Michael 11 Lamichhane, Bishnu Prasad 11 Miehe, Christian 11 Pani, Amiya Kumar 11 Zhang, Zhimin 10 Cai, Zhiqiang 10 Chen, Long 10 Chen, Yanping 10 Gopalakrishnan, Jay 10 Kochmann, Dennis M. 10 Meddahi, Salim 10 Nochetto, Ricardo Horacio 10 Rančić, Lidija Z. 10 Starke, Gerhard 10 Storn, Johannes 10 Wick, Thomas 10 Wriggers, Peter 9 Ainsworth, Mark 9 Aurada, Markus 9 Becker, Roland 9 Erath, Christoph 9 Haberl, Alexander 9 Herceg, Đorđe D. 9 Li, Jian 9 Liu, Jiangguo 9 Porwal, Kamana 9 Sauter, Stefan 9 Stein, Erwin 9 Zeng, Shengda 9 Zhang, Shun 9 Zhong, Liuqiang 8 Beirão da Veiga, Lourenço 8 Bringmann, Philipp 8 Dond, Asha K. 8 Eigel, Martin 8 Georgoulis, Emmanuil H. 8 Hinze, Michael 8 Hsiao, George Chia-Chu 8 Innerberger, Michael 8 Junker, Philipp 8 Keith, Brendan 8 Larson, Mats G. 8 Mao, Shipeng 8 Neff, Patrizio ...and 2,047 more Authors all top 5 Cited in 219 Serials 223 Computer Methods in Applied Mechanics and Engineering 145 Computers & Mathematics with Applications 144 Numerische Mathematik 113 Journal of Computational and Applied Mathematics 88 Journal of Scientific Computing 82 Mathematics of Computation 77 Computational Methods in Applied Mathematics 71 Applied Numerical Mathematics 70 SIAM Journal on Numerical Analysis 51 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 49 Numerical Methods for Partial Differential Equations 41 Journal of Computational Physics 40 Applied Mathematics and Computation 36 International Journal for Numerical Methods in Engineering 36 SIAM Journal on Scientific Computing 35 Computational Mechanics 28 M\(^3\)AS. 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Series A 2 Computational Mathematics and Modeling ...and 119 more Serials all top 5 Cited in 45 Fields 1,638 Numerical analysis (65-XX) 787 Partial differential equations (35-XX) 628 Mechanics of deformable solids (74-XX) 303 Fluid mechanics (76-XX) 231 Calculus of variations and optimal control; optimization (49-XX) 89 Optics, electromagnetic theory (78-XX) 59 Functions of a complex variable (30-XX) 47 Field theory and polynomials (12-XX) 38 Real functions (26-XX) 38 Approximations and expansions (41-XX) 36 Operator theory (47-XX) 33 Statistical mechanics, structure of matter (82-XX) 25 Integral equations (45-XX) 24 Potential theory (31-XX) 24 Computer science (68-XX) 23 Operations research, mathematical programming (90-XX) 19 Probability theory and stochastic processes (60-XX) 17 Classical thermodynamics, heat transfer (80-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 14 Functional analysis (46-XX) 13 General and overarching topics; collections (00-XX) 12 Global analysis, analysis on manifolds (58-XX) 11 Biology and other natural sciences (92-XX) 10 Information and communication theory, circuits (94-XX) 9 Ordinary differential equations (34-XX) 8 Systems theory; control (93-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Mechanics of particles and systems (70-XX) 6 Quantum theory (81-XX) 6 Geophysics (86-XX) 5 History and biography (01-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Special functions (33-XX) 3 Commutative algebra (13-XX) 3 Measure and integration (28-XX) 3 Differential geometry (53-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Combinatorics (05-XX) 2 Statistics (62-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Integral transforms, operational calculus (44-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX) Citations by Year