Cockburn, Bernardo

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 Author ID: cockburn.bernardo Published as: Cockburn, Bernardo; Cockburn, B. Homepage: http://www.math.umn.edu/~bcockbur// External Links: MGP · ORCID · ResearchGate · dblp
 Documents Indexed: 196 Publications since 1980, including 1 Book 2 Contributions as Editor Biographic References: 1 Publication Co-Authors: 116 Co-Authors with 183 Joint Publications 4,295 Co-Co-Authors
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Co-Authors

 14 single-authored 17 Nguyen, Ngoc Cuong 16 Shu, Chi-Wang 13 Gopalakrishnan, Jayadeep 13 Schötzau, Dominik 11 Fu, Guosheng 10 Guzmán, Johnny 8 Dong, Bo 8 Gremaud, Pierre-Alain 8 Kanschat, Guido 8 Sayas, Francisco-Javier 8 Shi, Ke 7 Qiu, Weifeng 7 Stolarski, Henryk K. 6 Celiker, Fatih 5 Chen, Yanlai 5 Reitich, Fernando 5 Sánchez, Manuel A. 4 Solano, Manuel E. 4 Zhang, Wujun 3 Brezzi, Franco 3 Castillo, Paul E. 3 Chen, Zhangxin 3 Dawson, Clint N. 3 Gripenberg, Gustaf 3 Güzey, Sukru 3 Marini, Luisa Donatella 3 Perugia, Ilaria 3 Qian, Jianliang 3 Rhebergen, Sander 3 Singler, John R. 3 Süli, Endre E. 3 Wang, Haiying 3 Xia, Shiqiang 3 Zhang, Yangwen 2 Albert, Samuel 2 Arnold, Douglas Norman 2 Çeşmelioğlu, Ayçıl 2 Chavent, Guy 2 Chen, Gang 2 Chung, Tsz Shun Eric 2 Coquel, Frédéric 2 Cui, Jintao 2 French, Donald A. 2 Gau, Huiing 2 Jerome, Joseph W. 2 Joly, Patrick 2 Jones, Don A. 2 Karniadakis, George Em 2 LeFloch, Philippe Gerard 2 Li, Fengyan 2 Londen, Stig-Olof 2 Luskin, Mitchell 2 Mustapha, Kassem 2 Peraire, Jaime 2 Peraire, Jaume 2 Peterson, Todd E. 2 Schwab, Christoph 2 Shen, Jiguang 2 Titi, Edriss Saleh 2 Triandaf, Ioana 2 Wang, Jing 2 Yang, Jimmy Xiangrong 2 Yenikaya, Bayram 1 Adams, Scot 1 Aizinger, Vadym 1 Bamberger, Alain 1 Benítez, Marta 1 Bourgeat, Alain P. 1 Bustinza, Rommel A. 1 Carrero, Jesús 1 Chabaud, Brandon M. 1 Chen, Min-Hung 1 Ciuca, C. 1 Claeyssen, Julio Ruiz 1 Demlow, Alan 1 Di Pietro, Daniele Antonio 1 Du, Shukai 1 Ern, Alexandre 1 Fu, Zhixing 1 Gardner, Carl L. 1 Gatica, Gabriel N. 1 Gupta, Deepa 1 Hou, Suchung 1 Hughes, Thomas J. R. 1 Hungria, Allan 1 Ichikawa, Ryuhei 1 Jaffré, Jérôme 1 Ji, Liangyue 1 Kabaria, Hardik 1 Kanapady, Ramdev 1 Kao, Chiu-Yen 1 Kern, Michel 1 Kirby, Robert M. II 1 Lazarov, Raytcho D. 1 Lew, Adrian J. 1 Lin, Sanyih 1 Merev, Ivan 1 Nochetto, Ricardo Horacio 1 Nour, Maher 1 Quarteroni, Alfio M. ...and 17 more Co-Authors
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Serials

 39 Mathematics of Computation 31 SIAM Journal on Numerical Analysis 26 Journal of Scientific Computing 21 Journal of Computational Physics 10 Computer Methods in Applied Mechanics and Engineering 9 IMA Journal of Numerical Analysis 5 SIAM Journal on Scientific Computing 3 International Journal for Numerical Methods in Engineering 3 Journal of Differential Equations 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Computers and Fluids 2 Numerische Mathematik 2 SIAM Journal on Scientific and Statistical Computing 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Comptes Rendus de l’Académie des Sciences. Série I 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Journal of Computational and Applied Mathematics 1 Applied Numerical Mathematics 1 SIAM Journal on Mathematical Analysis 1 Communications in Numerical Methods in Engineering 1 Computational and Applied Mathematics 1 Advances in Computational Mathematics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Computational Geosciences 1 Acta Numerica 1 GAMM-Mitteilungen 1 Lecture Notes in Mathematics 1 Lecture Notes in Computational Science and Engineering 1 S$$\vec{\text{e}}$$MA Journal 1 Communications on Applied Mathematics and Computation 1 Results in Applied Mathematics
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Fields

 177 Numerical analysis (65-XX) 113 Partial differential equations (35-XX) 47 Fluid mechanics (76-XX) 22 Mechanics of deformable solids (74-XX) 14 Optics, electromagnetic theory (78-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Operator theory (47-XX) 2 General and overarching topics; collections (00-XX) 2 Real functions (26-XX) 2 Ordinary differential equations (34-XX) 2 Functional analysis (46-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX)

Citations contained in zbMATH Open

182 Publications have been cited 12,216 times in 4,454 Documents Cited by Year
Unified analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1008.65080
Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, L. Donatella
2002
The local discontinuous Galerkin method for time-dependent convection-diffusion systems. Zbl 0927.65118
Cockburn, Bernardo; Shu, Chi-Wang
1998
TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II: General framework. Zbl 0662.65083
Cockburn, Bernardo; Shu, Chi-Wang
1989
The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems. Zbl 0920.65059
Cockburn, Bernardo; Shu, Chi-Wang
1998
Runge–Kutta discontinuous Galerkin methods for convection-dominated problems. Zbl 1065.76135
Cockburn, Bernardo; Shu, Chi-Wang
2001
TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems. Zbl 0677.65093
Cockburn, Bernardo; Lin, San-Yih; Shu, Chi-Wang
1989
The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV: The multidimensional case. Zbl 0695.65066
Cockburn, Bernardo; Hou, Suchung; Shu, Chi-Wang
1990
Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. Zbl 1205.65312
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Lazarov, Raytcho
2009
The development of discontinuous Galerkin methods. Zbl 0989.76045
Cockburn, Bernardo; Karniadakis, George E.; Shu, Chi-Wang
2000
The Runge-Kutta local projection $$P^ 1$$-discontinuous-Galerkin finite element method for scalar conservation laws. Zbl 0732.65094
Cockburn, Bernardo; Shu, Chi-Wang
1991
An a priori error analysis of the local discontinuous Galerkin method for elliptic problems. Zbl 0987.65111
Castillo, Paul; Cockburn, Bernardo; Perugia, Ilaria; Schötzau, Dominik
2000
Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids. Zbl 1041.65080
Cockburn, Bernardo; Kanschat, Guido; Perugia, Ilaria; Schötzau, Dominik
2001
A locally conservative LDG method for the incompressible Navier-Stokes equations. Zbl 1069.76029
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
2005
A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. Zbl 1198.65193
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
2008
A projection-based error analysis of HDG methods. Zbl 1197.65173
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Sayas, Francisco-Javier
2010
An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. Zbl 1187.65110
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2008
Discontinuous Galerkin methods for convection-dominated problems. Zbl 0937.76049
Cockburn, Bernardo
1999
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations. Zbl 1049.78019
Cockburn, Bernardo; Li, Fengyan; Shu, Chi-Wang
2004
Local discontinuous Galerkin methods for the Stokes system. Zbl 1032.65127
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik; Schwab, Christoph
2002
An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. Zbl 1391.76353
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2011
Optimal a priori error estimates for the $$hp$$-version of the local discontinuous Galerkin method for convection-diffusion problems. Zbl 0997.65111
Castillo, Paul; Cockburn, Bernardo; Schötzau, Dominik; Schwab, Christoph
2002
A hybridizable discontinuous Galerkin method for Stokes flow. Zbl 1227.76036
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2010
A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations. Zbl 1151.76527
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
2007
Analysis of HDG methods for Stokes flow. Zbl 1410.76164
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Nguyen, Ngoc Cuong; Peraire, Jaume; Sayas, Francisco-Javier
2011
Superconvergent discontinuous Galerkin methods for second-order elliptic problems. Zbl 1198.65194
Cockburn, Bernardo; Guzmán, Johnny; Wang, Haiying
2009
An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. Zbl 1177.65150
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2009
Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. Zbl 1341.65045
Cockburn, Bernardo; Di Pietro, Daniele A.; Ern, Alexandre
2016
Discontinuous Galerkin methods. Zbl 1036.65079
Cockburn, Bernardo
2003
A hybridizable discontinuous Galerkin method for steady-state convection-diffusion-reaction problems. Zbl 1200.65093
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny; Restelli, Marco; Sacco, Riccardo
2009
Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Zbl 1015.65049
Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre
2003
To CG or to HDG: A comparative study. Zbl 1244.65174
Kirby, Robert M.; Sherwin, Spencer J.; Cockburn, Bernardo
2012
Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127
Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella
2000
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. Zbl 1364.76093
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2011
Superconvergence of the numerical traces of discontinuous Galerkin and hybridized methods for convection-diffusion problems in one space dimension. Zbl 1109.65078
Celiker, Fatih; Cockburn, Bernardo
2007
A characterization of hybridized mixed methods for second order elliptic problems. Zbl 1084.65113
2004
Stabilization mechanisms in discontinuous Galerkin finite element methods. Zbl 1125.65102
Brezzi, F.; Cockburn, B.; Marini, L. D.; Süli, E.
2006
A new elasticity element made for enforcing weak stress symmetry. Zbl 1369.74078
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Guzmán, Johnny
2010
A hybridizable discontinuous Galerkin method for linear elasticity. Zbl 1176.74196
Soon, S.-C.; Cockburn, B.; Stolarski, Henryk K.
2009
The derivation of hybridizable discontinuous Galerkin methods for Stokes flow. Zbl 1279.76016
2009
Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell’s equations. Zbl 1230.78031
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2011
Nonlinearly stable compact schemes for shock calculations. Zbl 0805.65085
Cockburn, Bernardo; Shu, Chi-Wang
1994
Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24–26, 1999. Zbl 0935.00043
2000
A mixed finite element method for elasticity in three dimensions. Zbl 1125.74382
2005
Conditions for superconvergence of HDG methods for second-order elliptic problems. Zbl 1251.65158
Cockburn, Bernardo; Qiu, Weifeng; Shi, Ke
2012
An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems. Zbl 1143.76031
Cockburn, Bernardo; Dong, Bo
2007
An introduction to the discontinuous Galerkin method for convection-dominated problems. Zbl 0927.65120
Cockburn, Bernardo
1998
Hybridized globally divergence-free LDG methods. I: The Stokes problem. Zbl 1087.76061
Carrero, Jesús; Cockburn, Bernardo; Schötzau, Dominik
2006
Divergence-conforming HDG methods for Stokes flows. Zbl 1427.76125
Cockburn, Bernardo; Sayas, Francisco-Javier
2014
A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains. Zbl 1426.76298
Rhebergen, Sander; Cockburn, Bernardo
2012
The local discontinuous Galerkin method for the Oseen equations. Zbl 1066.76036
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
2004
A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations. Zbl 1286.76033
Rhebergen, Sander; Cockburn, Bernardo; van der Vegt, Jaap J. W.
2013
Some extensions of the local discontinuous Galerkin method for convection-diffusion equations in multidimensions. Zbl 0960.65107
Cockburn, Bernardo; Dawson, Clint
2000
Continuous dependence on the nonlinearities of solutions of degenerate parabolic equations. Zbl 0921.35017
Cockburn, B.; Gripenberg, G.
1999
Optimal convergence of the original DG method for the transport-reaction equation on special meshes. Zbl 1168.65058
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
2008
Incompressible finite elements via hybridization. I: The Stokes system in two space dimensions. Zbl 1145.76402
2005
Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems. Zbl 0866.35091
Cockburn, Bernardo; Jones, Don A.; Titi, Edriss S.
1997
Superconvergent HDG methods for linear elasticity with weakly symmetric stresses. Zbl 1441.74235
Cockburn, Bernardo; Shi, Ke
2013
An error estimate for finite volume methods for multidimensional conservation laws. Zbl 0855.65103
Cockburn, Bernardo; Coquel, Frédéric; LeFloch, Philippe
1994
Error estimates for finite element methods for scalar conservation laws. Zbl 0861.65077
Cockburn, Bernardo; Gremaud, Pierre-Alain
1996
Convergence of the finite volume method for multidimensional conservation laws. Zbl 0845.65051
Cockburn, B.; Coquel, F.; LeFloch, P. G.
1995
Analysis of variable-degree HDG methods for convection-diffusion equations. I: General nonconforming meshes. Zbl 1277.65094
Chen, Yanlai; Cockburn, Bernardo
2012
Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations. Zbl 1422.65377
Cesmelioglu, Aycil; Cockburn, Bernardo; Qiu, Weifeng
2017
An a posteriori error estimate for the local discontinuous Galerkin method applied to linear and nonlinear diffusion problems. Zbl 1065.76133
Bustinza, Rommel; Gatica, Gabriel N.; Cockburn, Bernardo
2005
A comparison of HDG methods for Stokes flow. Zbl 1203.76079
Cockburn, B.; Nguyen, N. C.; Peraire, J.
2010
A hybridizable discontinuous Galerkin formulation for non-linear elasticity. Zbl 1423.74895
Kabaria, Hardik; Lew, Adrian J.; Cockburn, Bernardo
2015
Discontinuous Galerkin methods for incompressible elastic materials. Zbl 1128.74041
Cockburn, Bernardo; Schötzau, Dominik; Wang, Jing
2006
An analysis of the embedded discontinuous Galerkin method for second-order elliptic problems. Zbl 1211.65153
Cockburn, Bernardo; Guzmán, Johnny; Soon, See-Chew; Stolarski, Henry K.
2009
The embedded discontinuous Galerkin method: application to linear shell problems. Zbl 1194.74403
Güzey, S.; Cockburn, B.; Stolarski, H. K.
2007
Locally conservative fluxes for the continuous Galerkin method. Zbl 1155.65100
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Wang, Haiying
2007
High-order RKDG methods for computational electromagnetics. Zbl 1091.78015
Chen, Min-Hung; Cockburn, Bernardo; Reitich, Fernando
2005
The local discontinuous Galerkin method for linearized incompressible fluid flow: a review. Zbl 1138.76382
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
2005
A hybridizable and superconvergent discontinuous Galerkin method for biharmonic problems. Zbl 1203.65249
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
2009
A hybridizable discontinuous Galerkin method for fractional diffusion problems. Zbl 1329.26013
Cockburn, Bernardo; Mustapha, Kassem
2015
The local projection $$P^ 0-P^ 1$$-discontinuous-Galerkin finite element method for scalar conservation laws. Zbl 0715.65079
Chavent, Guy; Cockburn, Bernardo
1989
Multigrid for an HDG method. Zbl 1304.65260
Cockburn, B.; Dubois, O.; Gopalakrishnan, J.; Tan, S.
2014
Uniform-in-time superconvergence of HDG methods for the heat equation. Zbl 1251.65138
Chabaud, Brandon; Cockburn, Bernardo
2012
Devising discontinuous Galerkin methods for nonlinear hyperbolic conservation laws. Zbl 0974.65092
Cockburn, Bernardo
2001
Error analysis of variable degree mixed methods for elliptic problems via hybridization. Zbl 1078.65093
2005
Static condensation, hybridization, and the devising of the HDG methods. Zbl 1357.65256
Cockburn, Bernardo
2016
Incompressible finite elements via hybridization. II: The Stokes system in three space dimensions. Zbl 1145.76403
2005
Superconvergence by $$M$$-decompositions. I: General theory for HDG methods for diffusion. Zbl 1361.65084
Cockburn, Bernardo; Fu, Guosheng; Sayas, Francisco Javier
2017
Hybridizable discontinuous Galerkin methods. Zbl 1216.65160
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2011
Conditions for superconvergence of HDG methods for Stokes flow. Zbl 1322.65104
Cockburn, Bernardo; Shi, Ke
2013
Advanced numerical approximation of nonlinear hyperbolic equations. Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (C. I. M. E.) held in Cetraro, Italy, June 23–28, 1997. Zbl 0904.00047
Cockburn, B.; Johnson, C.; Shu, C.-W.; Tadmor, E.
1998
An equal-order DG method for the incompressible Navier-Stokes equations. Zbl 1203.76080
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
2009
Analysis of HDG methods for Oseen equations. Zbl 1366.76048
Cesmelioglu, Aycil; Cockburn, Bernardo; Nguyen, Ngoc Cuong; Peraire, Jaume
2013
Devising $$\mathbf{HDG}$$ methods for Stokes flow: an overview. Zbl 1391.76315
Cockburn, Bernardo; Shi, Ke
2014
Local derivative post-processing for the discontinuous Galerkin method. Zbl 1176.65108
Ryan, Jennifer K.; Cockburn, Bernardo
2009
A posteriori error estimates for HDG methods. Zbl 1260.65099
Cockburn, Bernardo; Zhang, Wujun
2012
A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity. Zbl 1290.65110
Cockburn, Bernardo; Qiu, Weifeng; Solano, Manuel
2014
An explicit hybridizable discontinuous Galerkin method for the acoustic wave equation. Zbl 1423.76280
Stanglmeier, M.; Nguyen, N. C.; Peraire, J.; Cockburn, B.
2016
Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode. Zbl 0833.76033
Chen, Zhangxin; Cockburn, Bernardo; Gardner, Carl L.; Jerome, Joseph W.
1995
Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation. Zbl 1281.65118
Cockburn, Bernardo; Quenneville-Bélair, Vincent
2014
The staggered DG method is the limit of a hybridizable DG method. Zbl 1298.65168
Chung, Eric; Cockburn, Bernardo; Fu, Guosheng
2014
Analysis of variable-degree HDG methods for convection-diffusion equations. II: Semimatching nonconforming meshes. Zbl 1457.65187
Chen, Yanlai; Cockburn, Bernardo
2014
A posteriori error analysis for hybridizable discontinuous Galerkin methods for second-order elliptic problems. Zbl 1277.65089
Cockburn, Bernardo; Zhang, Wujun
2013
A phase-based hybridizable discontinuous Galerkin method for the numerical solution of the Helmholtz equation. Zbl 1349.78071
Nguyen, N. C.; Peraire, J.; Reitich, F.; Cockburn, B.
2015
Locking-free optimal discontinuous Galerkin methods for Timoshenko beams. Zbl 1127.74041
Celiker, Fatih; Cockburn, Bernardo; Stolarski, Henryk K.
2006
Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains. Zbl 1238.65111
Cockburn, Bernardo; Solano, Manuel
2012
Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems. Zbl 1339.26021
Mustapha, Kassem; Nour, Maher; Cockburn, Bernardo
2016
Symplectic Hamiltonian finite element methods for linear elastodynamics. Zbl 07414362
Sánchez, Manuel A.; Cockburn, Bernardo; Nguyen, Ngoc-Cuong; Peraire, Jaime
2021
Interpolatory HDG method for parabolic semilinear PDEs. Zbl 1422.65252
Cockburn, Bernardo; Singler, John R.; Zhang, Yangwen
2019
Superconvergent interpolatory HDG methods for reaction diffusion equations. I: An $$HDG_k$$ method. Zbl 1461.76345
Chen, Gang; Cockburn, Bernardo; Singler, John; Zhang, Yangwen
2019
An algorithm for stabilizing hybridizable discontinuous Galerkin methods for nonlinear elasticity. Zbl 1451.74205
Cockburn, Bernardo; Shen, Jiguang
2019
Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by $$M$$-decompositions. Zbl 1477.65205
Cockburn, Bernardo; Fu, Guosheng
2018
Stormer-Numerov HDG methods for acoustic waves. Zbl 1398.65248
Cockburn, Bernardo; Fu, Zhixing; Hungria, Allan; Ji, Liangyue; Sánchez, Manuel A.; Sayas, Francisco-Javier
2018
An introduction to the theory of $$M$$-decompositions. Zbl 1416.65412
Cockburn, Bernardo; Fu, Guosheng; Shi, Ke
2018
Supercloseness of primal-dual Galerkin approximations for second order elliptic problems. Zbl 1398.65294
Cockburn, Bernardo; Sánchez, Manuel A.; Xiong, Chunguang
2018
Discrete $$H^1$$-inequalities for spaces admitting M-decompositions. Zbl 1407.65285
Cockburn, Bernardo; Fu, Guosheng; Qiu, Weifeng
2018
Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations. Zbl 1422.65377
Cesmelioglu, Aycil; Cockburn, Bernardo; Qiu, Weifeng
2017
Superconvergence by $$M$$-decompositions. I: General theory for HDG methods for diffusion. Zbl 1361.65084
Cockburn, Bernardo; Fu, Guosheng; Sayas, Francisco Javier
2017
Superconvergence by $$M$$-decompositions. III: Construction of three-dimensional finite elements. Zbl 1412.65137
Cockburn, Bernardo; Fu, Guosheng
2017
Superconvergence by $$M$$-decompositions. II: Construction of two-dimensional finite elements. Zbl 1412.65205
Cockburn, Bernardo; Fu, Guosheng
2017
Symplectic Hamiltonian HDG methods for wave propagation phenomena. Zbl 1380.65421
Sánchez, M. A.; Ciuca, C.; Nguyen, N. C.; Peraire, J.; Cockburn, B.
2017
A note on the devising of superconvergent HDG methods for Stokes flow by $$M$$-decompositions. Zbl 1433.76077
Cockburn, Bernardo; Fu, Guosheng; Qiu, Weifeng
2017
A systematic construction of finite element commuting exact sequences. Zbl 1369.65145
Cockburn, Bernardo; Fu, Guosheng
2017
Adjoint-based, superconvergent Galerkin approximations of linear functionals. Zbl 1382.35097
Cockburn, Bernardo; Wang, Zhu
2017
Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. Zbl 1341.65045
Cockburn, Bernardo; Di Pietro, Daniele A.; Ern, Alexandre
2016
Static condensation, hybridization, and the devising of the HDG methods. Zbl 1357.65256
Cockburn, Bernardo
2016
An explicit hybridizable discontinuous Galerkin method for the acoustic wave equation. Zbl 1423.76280
Stanglmeier, M.; Nguyen, N. C.; Peraire, J.; Cockburn, B.
2016
Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems. Zbl 1339.26021
Mustapha, Kassem; Nour, Maher; Cockburn, Bernardo
2016
A hybridizable discontinuous Galerkin method for the $$p$$-Laplacian. Zbl 1382.65383
Cockburn, Bernardo; Shen, Jiguang
2016
Superconvergent HDG methods for linear, stationary, third-order equations in one-space dimension. Zbl 1344.65070
Chen, Yanlai; Cockburn, Bernardo; Dong, Bo
2016
The staggered DG method is the limit of a hybridizable DG method. II: The Stokes flow. Zbl 1457.65188
Chung, Eric; Cockburn, Bernardo; Fu, Guosheng
2016
A new discontinuous Galerkin method, conserving the discrete $$H^{2}$$-norm, for third-order linear equations in one space dimension. Zbl 1433.65145
Chen, Yanlai; Cockburn, Bernardo; Dong, Bo
2016
Contraction property of adaptive hybridizable discontinuous Galerkin methods. Zbl 1332.65164
Cockburn, Bernardo; Nochetto, Ricardo H.; Zhang, Wujun
2016
Hybridizable discontinuous Galerkin and mixed finite element methods for elliptic problems on surfaces. Zbl 1416.65439
Cockburn, Bernardo; Demlow, Alan
2016
A hybridizable discontinuous Galerkin formulation for non-linear elasticity. Zbl 1423.74895
Kabaria, Hardik; Lew, Adrian J.; Cockburn, Bernardo
2015
A hybridizable discontinuous Galerkin method for fractional diffusion problems. Zbl 1329.26013
Cockburn, Bernardo; Mustapha, Kassem
2015
A phase-based hybridizable discontinuous Galerkin method for the numerical solution of the Helmholtz equation. Zbl 1349.78071
Nguyen, N. C.; Peraire, J.; Reitich, F.; Cockburn, B.
2015
Analysis of an HDG method for linear elasticity. Zbl 1352.74037
Fu, Guosheng; Cockburn, B.; Stolarski, H.
2015
A class of embedded discontinuous Galerkin methods for computational fluid dynamics. Zbl 1349.76245
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2015
Divergence-conforming HDG methods for Stokes flows. Zbl 1427.76125
Cockburn, Bernardo; Sayas, Francisco-Javier
2014
Multigrid for an HDG method. Zbl 1304.65260
Cockburn, B.; Dubois, O.; Gopalakrishnan, J.; Tan, S.
2014
Devising $$\mathbf{HDG}$$ methods for Stokes flow: an overview. Zbl 1391.76315
Cockburn, Bernardo; Shi, Ke
2014
A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity. Zbl 1290.65110
Cockburn, Bernardo; Qiu, Weifeng; Solano, Manuel
2014
Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation. Zbl 1281.65118
Cockburn, Bernardo; Quenneville-Bélair, Vincent
2014
The staggered DG method is the limit of a hybridizable DG method. Zbl 1298.65168
Chung, Eric; Cockburn, Bernardo; Fu, Guosheng
2014
Analysis of variable-degree HDG methods for convection-diffusion equations. II: Semimatching nonconforming meshes. Zbl 1457.65187
Chen, Yanlai; Cockburn, Bernardo
2014
Solving convection-diffusion problems on curved domains by extensions from subdomains. Zbl 1304.65246
Cockburn, Bernardo; Solano, Manuel
2014
An a posteriori error estimate for the variable-degree Raviart-Thomas method. Zbl 1296.65142
Cockburn, Bernardo; Zhang, Wujun
2014
Commuting diagrams for the TNT elements on cubes. Zbl 1290.65109
Cockburn, Bernardo; Qiu, Weifeng
2014
A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations. Zbl 1286.76033
Rhebergen, Sander; Cockburn, Bernardo; van der Vegt, Jaap J. W.
2013
Superconvergent HDG methods for linear elasticity with weakly symmetric stresses. Zbl 1441.74235
Cockburn, Bernardo; Shi, Ke
2013
Conditions for superconvergence of HDG methods for Stokes flow. Zbl 1322.65104
Cockburn, Bernardo; Shi, Ke
2013
Analysis of HDG methods for Oseen equations. Zbl 1366.76048
Cesmelioglu, Aycil; Cockburn, Bernardo; Nguyen, Ngoc Cuong; Peraire, Jaume
2013
A posteriori error analysis for hybridizable discontinuous Galerkin methods for second-order elliptic problems. Zbl 1277.65089
Cockburn, Bernardo; Zhang, Wujun
2013
Space-time hybridizable discontinuous Galerkin method for the advection-diffusion equation on moving and deforming meshes. Zbl 1273.65149
Rhebergen, Sander; Cockburn, Bernardo
2013
Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations. Zbl 1269.65086
Cockburn, Bernardo; Merev, Ivan; Qian, Jianliang
2013
To CG or to HDG: A comparative study. Zbl 1244.65174
Kirby, Robert M.; Sherwin, Spencer J.; Cockburn, Bernardo
2012
Conditions for superconvergence of HDG methods for second-order elliptic problems. Zbl 1251.65158
Cockburn, Bernardo; Qiu, Weifeng; Shi, Ke
2012
A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains. Zbl 1426.76298
Rhebergen, Sander; Cockburn, Bernardo
2012
Analysis of variable-degree HDG methods for convection-diffusion equations. I: General nonconforming meshes. Zbl 1277.65094
Chen, Yanlai; Cockburn, Bernardo
2012
Uniform-in-time superconvergence of HDG methods for the heat equation. Zbl 1251.65138
Chabaud, Brandon; Cockburn, Bernardo
2012
A posteriori error estimates for HDG methods. Zbl 1260.65099
Cockburn, Bernardo; Zhang, Wujun
2012
Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains. Zbl 1238.65111
Cockburn, Bernardo; Solano, Manuel
2012
Superconvergent HDG methods on isoparametric elements for second-order elliptic problems. Zbl 1256.65093
Cockburn, Bernardo; Qiu, Weifeng; Shi, Ke
2012
An analysis of HDG methods for the vorticity-velocity-pressure formulation of the Stokes problem in three dimensions. Zbl 1250.76131
Cockburn, Bernardo; Cui, Jintao
2012
A projection-based error analysis of HDG methods for Timoshenko beams. Zbl 1427.74163
Celiker, Fatih; Cockburn, Bernardo; Shi, Ke
2012
Coupling at a distance HDG and BEM. Zbl 1241.65105
Cockburn, Bernardo; Sayas, Francisco-Javier; Solano, Manuel
2012
The devising of symmetric couplings of boundary element and discontinuous Galerkin methods. Zbl 1250.65145
Cockburn, Bernardo; Sayas, Francisco-Javier
2012
Coupling of Raviart-Thomas and hybridizable discontinuous Galerkin methods with BEM. Zbl 1260.65101
Cockburn, Bernardo; Guzmán, Johnny; Sayas, Francisco-Javier
2012
Divergence-free HDG methods for the vorticity-velocity formulation of the Stokes problem. Zbl 1311.76054
Cockburn, Bernardo; Cui, Jintao
2012
An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. Zbl 1391.76353
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2011
Analysis of HDG methods for Stokes flow. Zbl 1410.76164
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Nguyen, Ngoc Cuong; Peraire, Jaume; Sayas, Francisco-Javier
2011
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. Zbl 1364.76093
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2011
Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell’s equations. Zbl 1230.78031
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2011
Hybridizable discontinuous Galerkin methods. Zbl 1216.65160
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2011
Numerical analysis and scientific computing the hybridizable discontinuous Galerkin methods. Zbl 1228.65221
Cockburn, Bernardo
2011
A projection-based error analysis of HDG methods. Zbl 1197.65173
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Sayas, Francisco-Javier
2010
A hybridizable discontinuous Galerkin method for Stokes flow. Zbl 1227.76036
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2010
A new elasticity element made for enforcing weak stress symmetry. Zbl 1369.74078
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Guzmán, Johnny
2010
A comparison of HDG methods for Stokes flow. Zbl 1203.76079
Cockburn, B.; Nguyen, N. C.; Peraire, J.
2010
Hybridizable discontinuous Galerkin methods for Timoshenko beams. Zbl 1203.74078
Celiker, Fatih; Cockburn, Bernardo; Shi, Ke
2010
Boundary-conforming discontinuous Galerkin methods via extensions from subdomains. Zbl 1203.65250
Cockburn, Bernardo; Gupta, Deepa; Reitich, Fernando
2010
Optimal convergence of the original DG method on special meshes for variable transport velocity. Zbl 1209.65123
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny; Qian, Jianliang
2010
Hybridization and postprocessing techniques for mixed eigenfunctions. Zbl 1220.65159
Cockburn, B.; Gopalakrishnan, J.; Li, F.; Nguyen, N.-C.; Peraire, J.
2010
Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. Zbl 1205.65312
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Lazarov, Raytcho
2009
Superconvergent discontinuous Galerkin methods for second-order elliptic problems. Zbl 1198.65194
Cockburn, Bernardo; Guzmán, Johnny; Wang, Haiying
2009
An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. Zbl 1177.65150
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2009
A hybridizable discontinuous Galerkin method for steady-state convection-diffusion-reaction problems. Zbl 1200.65093
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny; Restelli, Marco; Sacco, Riccardo
2009
A hybridizable discontinuous Galerkin method for linear elasticity. Zbl 1176.74196
Soon, S.-C.; Cockburn, B.; Stolarski, Henryk K.
2009
The derivation of hybridizable discontinuous Galerkin methods for Stokes flow. Zbl 1279.76016
2009
An analysis of the embedded discontinuous Galerkin method for second-order elliptic problems. Zbl 1211.65153
Cockburn, Bernardo; Guzmán, Johnny; Soon, See-Chew; Stolarski, Henry K.
2009
A hybridizable and superconvergent discontinuous Galerkin method for biharmonic problems. Zbl 1203.65249
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
2009
An equal-order DG method for the incompressible Navier-Stokes equations. Zbl 1203.76080
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
2009
Local derivative post-processing for the discontinuous Galerkin method. Zbl 1176.65108
Ryan, Jennifer K.; Cockburn, Bernardo
2009
Foreword: Discontinuous Galerkin methods for partial differential equations. Zbl 1203.65005
2009
A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. Zbl 1198.65193
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
2008
An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. Zbl 1187.65110
Nguyen, N. C.; Peraire, J.; Cockburn, B.
2008
Optimal convergence of the original DG method for the transport-reaction equation on special meshes. Zbl 1168.65058
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
2008
Error estimates for the Runge – Kutta discontinuous Galerkin method for the transport equation with discontinuous initial data. Zbl 1178.65107
Cockburn, Bernardo; Guzmán, Johnny
2008
The computation of a locally conservative stress for the continuous Galerkin method for compressible linearly elastic materials. Zbl 1203.74015
Cockburn, Bernardo; Wang, Haiying
2008
A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations. Zbl 1151.76527
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
2007
Superconvergence of the numerical traces of discontinuous Galerkin and hybridized methods for convection-diffusion problems in one space dimension. Zbl 1109.65078
Celiker, Fatih; Cockburn, Bernardo
2007
An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems. Zbl 1143.76031
Cockburn, Bernardo; Dong, Bo
2007
The embedded discontinuous Galerkin method: application to linear shell problems. Zbl 1194.74403
Güzey, S.; Cockburn, B.; Stolarski, H. K.
2007
Locally conservative fluxes for the continuous Galerkin method. Zbl 1155.65100
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Wang, Haiying
2007
An adaptive high-order discontinuous Galerkin method with error control for the Hamilton-Jacobi equations. I: The one-dimensional steady state case. Zbl 1126.65098
Chen, Yanlai; Cockburn, Bernardo
2007
Adjoint recovery of superconvergent linear functionals from Galerkin approximations. The one-dimensional case. Zbl 1134.65052
Cockburn, Bernardo; Ichikawa, Ryuhei
2007
...and 82 more Documents
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Cited by 4,608 Authors

 156 Shu, Chi-Wang 108 Cockburn, Bernardo 59 Dumbser, Michael 52 Qiu, Jianxian 50 Xu, Yan 41 Baccouch, Mahboub 38 Antonietti, Paola Francesca 38 Chung, Tsz Shun Eric 38 Dawson, Clint N. 38 Ye, Xiu 37 Di Pietro, Daniele Antonio 35 Cheng, Yingda 33 Ern, Alexandre 33 Qiu, Jingmei 32 Schötzau, Dominik 31 Li, Fengyan 30 Bassi, Francesco 30 Li, Jichun 30 Liu, Tiegang 29 Ryan, Jennifer K. 29 Xing, Yulong 29 Zhang, Shangyou 28 Houston, Paul 28 Liu, Hailiang 28 van der Vegt, Jaap J. W. 28 Yu, Xijun 26 Nguyen, Ngoc Cuong 26 Xia, Yinhua 24 Huang, Yunqing 24 Mu, Lin 24 Zhang, Qiang 23 Burman, Erik 23 Hesthaven, Jan S. 23 Munz, Claus-Dieter 23 Yang, Yang 22 Adjerid, Slimane 22 Fu, Guosheng 22 Jameson, Antony 22 Luo, Hong 22 Rivière, Beatrice M. 22 Zhang, Mengping 22 Zhang, Zhimin 21 He, Yinnian 20 Cheng, Jian 20 Crivellini, Andrea 20 Giani, Stefano 20 Kanschat, Guido 20 Kirby, Robert M. II 20 Perugia, Ilaria 20 Rhebergen, Sander 19 Balsara, Dinshaw S. 19 Dolejší, Vít 19 Huang, Xuehai 19 Wang, Junping 19 Xu, Kun 18 Gudi, Thirupathi 18 Karlsen, Kenneth Hvistendahl 18 Kubatko, Ethan J. 18 Marini, Luisa Donatella 18 Sayas, Francisco-Javier 18 Titi, Edriss Saleh 17 Feng, Minfu 17 Hughes, Thomas J. R. 17 Ruiz-Baier, Ricardo 17 Scovazzi, Guglielmo 17 Xu, Jinchao 17 Zhang, Yangwen 17 Zhu, Jun 16 Aizinger, Vadym 16 Bazilevs, Yuri 16 Beirão da Veiga, Lourenço 16 Brezzi, Franco 16 Castillo, Paul E. 16 Gassner, Gregor J. 16 Guzmán, Johnny 16 Nordström, Jan 16 Park, Eun-Jae 16 Solano, Manuel E. 16 Toro, Eleuterio F. 16 Wheeler, Mary Fanett 16 Wihler, Thomas Pascal 15 Feistauer, Miloslav 15 Guo, Wei 15 Huerta, Antonio 15 Kronbichler, Martin 15 Li, Maojun 15 Manzini, Gianmarco 15 Persson, Per-Olof 15 Qiu, Weifeng 15 Schütz, Jochen 15 Verani, Marco 15 Westerink, Joannes J. 14 Colombo, Alessandro G. 14 Ferrer, Esteban 14 Gatica, Gabriel N. 14 Ghidoni, Antonio 14 Lanteri, Stéphane 14 May, Georg 14 Rebay, Stefano 14 Schöberl, Joachim ...and 4,508 more Authors
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Cited in 249 Serials

 821 Journal of Computational Physics 553 Journal of Scientific Computing 331 Computer Methods in Applied Mechanics and Engineering 218 Computers and Fluids 180 Journal of Computational and Applied Mathematics 166 Computers & Mathematics with Applications 158 Mathematics of Computation 141 Applied Numerical Mathematics 115 SIAM Journal on Scientific Computing 106 SIAM Journal on Numerical Analysis 93 Applied Mathematics and Computation 86 Numerische Mathematik 68 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 65 Communications in Computational Physics 64 International Journal for Numerical Methods in Engineering 57 Numerical Methods for Partial Differential Equations 51 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 50 International Journal for Numerical Methods in Fluids 42 Communications on Applied Mathematics and Computation 31 Computational Methods in Applied Mathematics 30 Computational Geosciences 29 Advances in Computational Mathematics 26 Calcolo 25 Computational Mechanics 25 Advances in Applied Mathematics and Mechanics 24 Mathematics and Computers in Simulation 22 Applied Mathematical Modelling 22 International Journal of Computer Mathematics 22 International Journal of Numerical Analysis and Modeling 19 Applied Mathematics Letters 19 Numerical Algorithms 18 International Journal of Computational Fluid Dynamics 16 Journal of Mathematical Analysis and Applications 16 Computational and Applied Mathematics 16 Journal of Numerical Mathematics 14 BIT 13 Matematicheskoe Modelirovanie 13 Science China. Mathematics 12 Communications in Numerical Methods in Engineering 12 International Journal of Computational Methods 11 Journal of Differential Equations 11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Applicable Analysis 10 Computational Mathematics and Mathematical Physics 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Numerical Functional Analysis and Optimization 9 Physica D 9 Japan Journal of Industrial and Applied Mathematics 9 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 9 Discrete and Continuous Dynamical Systems. Series B 9 Electronic Research Archive 8 Applied Mathematics and Mechanics. (English Edition) 8 Applications of Mathematics 8 Mathematical Problems in Engineering 8 Communications in Nonlinear Science and Numerical Simulation 8 Differential Equations 8 Multiscale Modeling & Simulation 8 Journal of Hyperbolic Differential Equations 8 Boundary Value Problems 8 Results in Applied Mathematics 7 Mathematical Methods in the Applied Sciences 7 Mathematical and Computer Modelling 7 Computing and Visualization in Science 7 Archives of Computational Methods in Engineering 7 Journal of Applied Mathematics and Computing 7 Acta Mechanica Sinica 6 Computer Physics Communications 6 Journal of Computational Mathematics 6 ETNA. Electronic Transactions on Numerical Analysis 6 Engineering Analysis with Boundary Elements 6 Abstract and Applied Analysis 6 International Journal for Numerical Methods in Biomedical Engineering 6 GEM - International Journal on Geomathematics 6 Journal of the Korean Society for Industrial and Applied Mathematics 6 S$$\vec{\text{e}}$$MA Journal 5 RAIRO. Modélisation Mathématique et Analyse Numérique 5 Acta Mathematicae Applicatae Sinica. English Series 5 COMPEL 5 Communications in Partial Differential Equations 5 Numerical Linear Algebra with Applications 5 International Journal of Numerical Methods for Heat & Fluid Flow 5 Foundations of Computational Mathematics 5 Advances in Difference Equations 5 Numerical Mathematics: Theory, Methods and Applications 5 East Asian Journal on Applied Mathematics 5 SMAI Journal of Computational Mathematics 4 Archive for Rational Mechanics and Analysis 4 Journal of Engineering Mathematics 4 Journal of Fluid Mechanics 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 4 SIAM Journal on Applied Dynamical Systems 4 Acta Numerica 4 Advances in Mathematical Physics 4 Communications in Mathematics and Statistics 3 Journal of Mathematical Biology 3 Meccanica 3 Acta Applicandae Mathematicae 3 Journal of Nonlinear Science ...and 149 more Serials
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