Edit Profile (opens in new tab) Cockburn, Bernardo Co-Author Distance 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: 201 Publications since 1980, including 1 Book and 2 Additional arXiv Preprints 2 Contributions as Editor Biographic References: 1 Publication Co-Authors: 117 Co-Authors with 186 Joint Publications 4,137 Co-Co-Authors all top 5 Co-Authors 16 single-authored 17 Nguyen, Ngoc Cuong 16 Shu, Chi-Wang 13 Gopalakrishnan, Jay 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 Sánchez, Manuel A. 7 Stolarski, Henryk K. 6 Celiker, Fatih 5 Chen, Yanlai 5 Reitich, Fernando 4 Solano, Manuel E. 4 Zhang, Wujun 3 Brezzi, Franco 3 Castillo, Paul E. 3 Chen, Zhangxin 3 Dawson, Clint N. 3 Du, Shukai 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 Yang, Jimmy Xiangrong 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 Yenikaya, Bayram 1 Adams, Scot 1 Aizinger, Vadym 1 Anantharamu, Sreevatsa 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 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 ...and 18 more Co-Authors all top 5 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 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 International Journal for Numerical Methods in Engineering 3 Journal of Differential Equations 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 Japan Journal of Industrial and Applied 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 Computational Methods in Applied Mathematics 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 all top 5 Fields 180 Numerical analysis (65-XX) 115 Partial differential equations (35-XX) 47 Fluid mechanics (76-XX) 23 Mechanics of deformable solids (74-XX) 17 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 191 Publications have been cited 14,306 times in 5,209 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 1,389 2002 The local discontinuous Galerkin method for time-dependent convection-diffusion systems. Zbl 0927.65118 Cockburn, Bernardo; Shu, Chi-Wang 1,060 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 968 1989 The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems. Zbl 0920.65059 Cockburn, Bernardo; Shu, Chi-Wang 902 1998 Runge–Kutta discontinuous Galerkin methods for convection-dominated problems. Zbl 1065.76135 Cockburn, Bernardo; Shu, Chi-Wang 776 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 653 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 639 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 587 2009 The development of discontinuous Galerkin methods. Zbl 0989.76045 Cockburn, Bernardo; Karniadakis, George E.; Shu, Chi-Wang 354 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 277 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 254 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 177 2001 A locally conservative LDG method for the incompressible Navier-Stokes equations. Zbl 1069.76029 Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik 173 2005 A projection-based error analysis of HDG methods. Zbl 1197.65173 Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Sayas, Francisco-Javier 158 2010 A hybridizable discontinuous Galerkin method for Stokes flow. Zbl 1227.76036 Nguyen, N. C.; Peraire, J.; Cockburn, B. 155 2010 A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. Zbl 1198.65193 Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny 152 2008 An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. Zbl 1187.65110 Nguyen, N. C.; Peraire, J.; Cockburn, B. 147 2008 An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. Zbl 1391.76353 Nguyen, N. C.; Peraire, J.; Cockburn, B. 145 2011 A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations. Zbl 1151.76527 Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik 144 2007 Local discontinuous Galerkin methods for the Stokes system. Zbl 1032.65127 Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik; Schwab, Christoph 142 2002 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 139 2002 Discontinuous Galerkin methods for convection-dominated problems. Zbl 0937.76049 Cockburn, Bernardo 138 1999 Locally divergence-free discontinuous Galerkin methods for the Maxwell equations. Zbl 1049.78019 Cockburn, Bernardo; Li, Fengyan; Shu, Chi-Wang 132 2004 Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. Zbl 1341.65045 Cockburn, Bernardo; Di Pietro, Daniele A.; Ern, Alexandre 112 2016 Analysis of HDG methods for Stokes flow. Zbl 1410.76164 Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Nguyen, Ngoc Cuong; Peraire, Jaume; Sayas, Francisco-Javier 110 2011 Superconvergent discontinuous Galerkin methods for second-order elliptic problems. Zbl 1198.65194 Cockburn, Bernardo; Guzmán, Johnny; Wang, Haiying 108 2009 An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. Zbl 1177.65150 Nguyen, N. C.; Peraire, J.; Cockburn, B. 104 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 102 2009 Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24–26, 1999. Zbl 0935.00043 100 2000 Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Zbl 1015.65049 Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre 95 2003 Discontinuous Galerkin methods. Zbl 1036.65079 Cockburn, Bernardo 93 2003 To CG or to HDG: A comparative study. Zbl 1244.65174 Kirby, Robert M.; Sherwin, Spencer J.; Cockburn, Bernardo 85 2012 High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. Zbl 1364.76093 Nguyen, N. C.; Peraire, J.; Cockburn, B. 82 2011 A characterization of hybridized mixed methods for second order elliptic problems. Zbl 1084.65113 Cockburn, Bernardo; Gopalakrishnan, Jayadeep 77 2004 Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127 Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella 73 2000 A new elasticity element made for enforcing weak stress symmetry. Zbl 1369.74078 Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Guzmán, Johnny 73 2010 Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell’s equations. Zbl 1230.78031 Nguyen, N. C.; Peraire, J.; Cockburn, B. 72 2011 The derivation of hybridizable discontinuous Galerkin methods for Stokes flow. Zbl 1279.76016 Cockburn, Bernardo; Gopalakrishnan, Jayadeep 71 2009 A hybridizable discontinuous Galerkin method for linear elasticity. Zbl 1176.74196 Soon, S.-C.; Cockburn, B.; Stolarski, Henryk K. 70 2009 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 69 2007 An introduction to the discontinuous Galerkin method for convection-dominated problems. Zbl 0927.65120 Cockburn, Bernardo 66 1998 Stabilization mechanisms in discontinuous Galerkin finite element methods. Zbl 1125.65102 Brezzi, F.; Cockburn, B.; Marini, L. D.; Süli, E. 64 2006 Conditions for superconvergence of HDG methods for second-order elliptic problems. Zbl 1251.65158 Cockburn, Bernardo; Qiu, Weifeng; Shi, Ke 63 2012 An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems. Zbl 1143.76031 Cockburn, Bernardo; Dong, Bo 62 2007 Divergence-conforming HDG methods for Stokes flows. Zbl 1427.76125 Cockburn, Bernardo; Sayas, Francisco-Javier 60 2014 A mixed finite element method for elasticity in three dimensions. Zbl 1125.74382 Adams, Scot; Cockburn, Bernardo 59 2005 Hybridized globally divergence-free LDG methods. I: The Stokes problem. Zbl 1087.76061 Carrero, Jesús; Cockburn, Bernardo; Schötzau, Dominik 57 2006 Nonlinearly stable compact schemes for shock calculations. Zbl 0805.65085 Cockburn, Bernardo; Shu, Chi-Wang 55 1994 Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations. Zbl 1422.65377 Cesmelioglu, Aycil; Cockburn, Bernardo; Qiu, Weifeng 53 2017 A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains. Zbl 1426.76298 Rhebergen, Sander; Cockburn, Bernardo 52 2012 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. 52 2013 The local discontinuous Galerkin method for the Oseen equations. Zbl 1066.76036 Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik 51 2004 Static condensation, hybridization, and the devising of the HDG methods. Zbl 1357.65256 Cockburn, Bernardo 49 2016 Optimal convergence of the original DG method for the transport-reaction equation on special meshes. Zbl 1168.65058 Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny 46 2008 Continuous dependence on the nonlinearities of solutions of degenerate parabolic equations. Zbl 0921.35017 Cockburn, B.; Gripenberg, G. 43 1999 Incompressible finite elements via hybridization. I: The Stokes system in two space dimensions. Zbl 1145.76402 Cockburn, Bernardo; Gopalakrishnan, Jayadeep 43 2005 Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems. Zbl 0866.35091 Cockburn, Bernardo; Jones, Don A.; Titi, Edriss S. 43 1997 Superconvergent HDG methods for linear elasticity with weakly symmetric stresses. Zbl 1441.74235 Cockburn, Bernardo; Shi, Ke 43 2013 Some extensions of the local discontinuous Galerkin method for convection-diffusion equations in multidimensions. Zbl 0960.65107 Cockburn, Bernardo; Dawson, Clint 42 2000 Analysis of variable-degree HDG methods for convection-diffusion equations. I: General nonconforming meshes. Zbl 1277.65094 Chen, Yanlai; Cockburn, Bernardo 41 2012 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. 40 1998 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. 40 2009 A comparison of HDG methods for Stokes flow. Zbl 1203.76079 Cockburn, B.; Nguyen, N. C.; Peraire, J. 39 2010 Convergence of the finite volume method for multidimensional conservation laws. Zbl 0845.65051 Cockburn, B.; Coquel, F.; LeFloch, P. G. 39 1995 Locally conservative fluxes for the continuous Galerkin method. Zbl 1155.65100 Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Wang, Haiying 39 2007 A hybridizable discontinuous Galerkin formulation for non-linear elasticity. Zbl 1423.74895 Kabaria, Hardik; Lew, Adrian J.; Cockburn, Bernardo 39 2015 Multigrid for an HDG method. Zbl 1304.65260 Cockburn, B.; Dubois, O.; Gopalakrishnan, J.; Tan, S. 38 2014 The embedded discontinuous Galerkin method: application to linear shell problems. Zbl 1194.74403 Güzey, S.; Cockburn, B.; Stolarski, H. K. 38 2007 Error estimates for finite element methods for scalar conservation laws. Zbl 0861.65077 Cockburn, Bernardo; Gremaud, Pierre-Alain 37 1996 Uniform-in-time superconvergence of HDG methods for the heat equation. Zbl 1251.65138 Chabaud, Brandon; Cockburn, Bernardo 37 2012 An error estimate for finite volume methods for multidimensional conservation laws. Zbl 0855.65103 Cockburn, Bernardo; Coquel, Frédéric; LeFloch, Philippe 36 1994 Discontinuous Galerkin methods for incompressible elastic materials. Zbl 1128.74041 Cockburn, Bernardo; Schötzau, Dominik; Wang, Jing 35 2006 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 35 2005 The local projection \(P^ 0-P^ 1\)-discontinuous-Galerkin finite element method for scalar conservation laws. Zbl 0715.65079 Chavent, Guy; Cockburn, Bernardo 35 1989 A hybridizable and superconvergent discontinuous Galerkin method for biharmonic problems. Zbl 1203.65249 Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny 34 2009 The local discontinuous Galerkin method for linearized incompressible fluid flow: a review. Zbl 1138.76382 Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik 33 2005 Superconvergence by \(M\)-decompositions. I: General theory for HDG methods for diffusion. Zbl 1361.65084 Cockburn, Bernardo; Fu, Guosheng; Sayas, Francisco Javier 33 2017 Incompressible finite elements via hybridization. II: The Stokes system in three space dimensions. Zbl 1145.76403 Cockburn, Bernardo; Gopalakrishnan, Jayadeep 32 2005 High-order RKDG methods for computational electromagnetics. Zbl 1091.78015 Chen, Min-Hung; Cockburn, Bernardo; Reitich, Fernando 32 2005 A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity. Zbl 1290.65110 Cockburn, Bernardo; Qiu, Weifeng; Solano, Manuel 32 2014 A hybridizable discontinuous Galerkin method for fractional diffusion problems. Zbl 1329.26013 Cockburn, Bernardo; Mustapha, Kassem 31 2015 Hybridizable discontinuous Galerkin methods. Zbl 1216.65160 Nguyen, N. C.; Peraire, J.; Cockburn, B. 30 2011 Error analysis of variable degree mixed methods for elliptic problems via hybridization. Zbl 1078.65093 Cockburn, Bernardo; Gopalakrishnan, Jayadeep 30 2005 Analysis of HDG methods for Oseen equations. Zbl 1366.76048 Cesmelioglu, Aycil; Cockburn, Bernardo; Nguyen, Ngoc Cuong; Peraire, Jaume 30 2013 Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation. Zbl 1281.65118 Cockburn, Bernardo; Quenneville-Bélair, Vincent 30 2014 A posteriori error estimates for HDG methods. Zbl 1260.65099 Cockburn, Bernardo; Zhang, Wujun 29 2012 An equal-order DG method for the incompressible Navier-Stokes equations. Zbl 1203.76080 Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik 29 2009 Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains. Zbl 1238.65111 Cockburn, Bernardo; Solano, Manuel 29 2012 Devising discontinuous Galerkin methods for nonlinear hyperbolic conservation laws. Zbl 0974.65092 Cockburn, Bernardo 29 2001 An explicit hybridizable discontinuous Galerkin method for the acoustic wave equation. Zbl 1423.76280 Stanglmeier, M.; Nguyen, N. C.; Peraire, J.; Cockburn, B. 29 2016 Conditions for superconvergence of HDG methods for Stokes flow. Zbl 1322.65104 Cockburn, Bernardo; Shi, Ke 29 2013 Analysis of variable-degree HDG methods for convection-diffusion equations. II: Semimatching nonconforming meshes. Zbl 1457.65187 Chen, Yanlai; Cockburn, Bernardo 27 2014 Devising \(\mathbf{HDG}\) methods for Stokes flow: an overview. Zbl 1391.76315 Cockburn, Bernardo; Shi, Ke 27 2014 Local derivative post-processing for the discontinuous Galerkin method. Zbl 1176.65108 Ryan, Jennifer K.; Cockburn, Bernardo 26 2009 The staggered DG method is the limit of a hybridizable DG method. Zbl 1298.65168 Chung, Eric; Cockburn, Bernardo; Fu, Guosheng 26 2014 A posteriori error analysis for hybridizable discontinuous Galerkin methods for second-order elliptic problems. Zbl 1277.65089 Cockburn, Bernardo; Zhang, Wujun 26 2013 Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode. Zbl 0833.76033 Chen, Zhangxin; Cockburn, Bernardo; Gardner, Carl L.; Jerome, Joseph W. 24 1995 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. 24 2015 Locking-free optimal discontinuous Galerkin methods for Timoshenko beams. Zbl 1127.74041 Celiker, Fatih; Cockburn, Bernardo; Stolarski, Henryk K. 22 2006 A hybridizable discontinuous Galerkin method for the \(p\)-Laplacian. Zbl 1382.65383 Cockburn, Bernardo; Shen, Jiguang 22 2016 The pursuit of a dream, Francisco Javier Sayas and the HDG methods. Zbl 1484.01023 Cockburn, Bernardo 4 2022 Discontinuous Galerkin methods through the Lens of variational multiscale analysis. Zbl 1507.76123 Stoter, Stein K. F.; Cockburn, Bernardo; Hughes, Thomas J. R.; Schillinger, Dominik 3 2022 Discontinuous Galerkin methods with time-operators in their numerical traces for time-dependent electromagnetics. Zbl 1497.65167 Cockburn, Bernardo; Du, Shukai; Sánchez, Manuel A. 2 2022 An adjoint-based adaptive error approximation of functionals by the hybridizable discontinuous Galerkin method for second-order elliptic equations. Zbl 1515.65288 Cockburn, Bernardo; Xia, Shiqiang 1 2022 An a priori error analysis of adjoint-based super-convergent Galerkin approximations of linear functionals. Zbl 1522.65205 Cockburn, Bernardo; Xia, Shiqiang 1 2022 An adjoint-based super-convergent Galerkin approximation of eigenvalues. Zbl 07524805 Cockburn, Bernardo; Xia, Shiqiang 1 2022 Symplectic Hamiltonian finite element methods for electromagnetics. Zbl 1507.74509 Sánchez, Manuel A.; Du, Shukai; Cockburn, Bernardo; Nguyen, Ngoc-Cuong; Peraire, Jaime 1 2022 Post-processing for spatial accuracy-enhancement of pure Lagrange-Galerkin schemes applied to convection-diffusion equations. Zbl 07465492 Benítez, Marta; Cockburn, Bernardo 1 2022 Symplectic Hamiltonian finite element methods for linear elastodynamics. Zbl 1506.74438 Sánchez, Manuel A.; Cockburn, Bernardo; Nguyen, Ngoc-Cuong; Peraire, Jaime 5 2021 Interpolatory HDG method for parabolic semilinear PDEs. Zbl 1422.65252 Cockburn, Bernardo; Singler, John R.; Zhang, Yangwen 15 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 8 2019 An algorithm for stabilizing hybridizable discontinuous Galerkin methods for nonlinear elasticity. Zbl 1451.74205 Cockburn, Bernardo; Shen, Jiguang 4 2019 Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by \(M\)-decompositions. Zbl 1477.65205 Cockburn, Bernardo; Fu, Guosheng 21 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 16 2018 Supercloseness of primal-dual Galerkin approximations for second order elliptic problems. Zbl 1398.65294 Cockburn, Bernardo; Sánchez, Manuel A.; Xiong, Chunguang 2 2018 An introduction to the theory of \(M\)-decompositions. Zbl 1416.65412 Cockburn, Bernardo; Fu, Guosheng; Shi, Ke 2 2018 Discrete \(H^1\)-inequalities for spaces admitting M-decompositions. Zbl 1407.65285 Cockburn, Bernardo; Fu, Guosheng; Qiu, Weifeng 2 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 53 2017 Superconvergence by \(M\)-decompositions. I: General theory for HDG methods for diffusion. Zbl 1361.65084 Cockburn, Bernardo; Fu, Guosheng; Sayas, Francisco Javier 33 2017 Superconvergence by \(M\)-decompositions. II: Construction of two-dimensional finite elements. Zbl 1412.65205 Cockburn, Bernardo; Fu, Guosheng 21 2017 Symplectic Hamiltonian HDG methods for wave propagation phenomena. Zbl 1380.65421 Sánchez, M. A.; Ciuca, C.; Nguyen, N. C.; Peraire, J.; Cockburn, B. 20 2017 Superconvergence by \(M\)-decompositions. III: Construction of three-dimensional finite elements. Zbl 1412.65137 Cockburn, Bernardo; Fu, Guosheng 20 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 20 2017 A systematic construction of finite element commuting exact sequences. Zbl 1369.65145 Cockburn, Bernardo; Fu, Guosheng 13 2017 Adjoint-based, superconvergent Galerkin approximations of linear functionals. Zbl 1382.35097 Cockburn, Bernardo; Wang, Zhu 7 2017 Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. Zbl 1341.65045 Cockburn, Bernardo; Di Pietro, Daniele A.; Ern, Alexandre 112 2016 Static condensation, hybridization, and the devising of the HDG methods. Zbl 1357.65256 Cockburn, Bernardo 49 2016 An explicit hybridizable discontinuous Galerkin method for the acoustic wave equation. Zbl 1423.76280 Stanglmeier, M.; Nguyen, N. C.; Peraire, J.; Cockburn, B. 29 2016 A hybridizable discontinuous Galerkin method for the \(p\)-Laplacian. Zbl 1382.65383 Cockburn, Bernardo; Shen, Jiguang 22 2016 Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems. Zbl 1339.26021 Mustapha, Kassem; Nour, Maher; Cockburn, Bernardo 21 2016 Superconvergent HDG methods for linear, stationary, third-order equations in one-space dimension. Zbl 1344.65070 Chen, Yanlai; Cockburn, Bernardo; Dong, Bo 15 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 12 2016 Contraction property of adaptive hybridizable discontinuous Galerkin methods. Zbl 1332.65164 Cockburn, Bernardo; Nochetto, Ricardo H.; Zhang, Wujun 10 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 9 2016 Hybridizable discontinuous Galerkin and mixed finite element methods for elliptic problems on surfaces. Zbl 1416.65439 Cockburn, Bernardo; Demlow, Alan 5 2016 A hybridizable discontinuous Galerkin formulation for non-linear elasticity. Zbl 1423.74895 Kabaria, Hardik; Lew, Adrian J.; Cockburn, Bernardo 39 2015 A hybridizable discontinuous Galerkin method for fractional diffusion problems. Zbl 1329.26013 Cockburn, Bernardo; Mustapha, Kassem 31 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. 24 2015 Analysis of an HDG method for linear elasticity. Zbl 1352.74037 Fu, Guosheng; Cockburn, B.; Stolarski, H. 21 2015 A class of embedded discontinuous Galerkin methods for computational fluid dynamics. Zbl 1349.76245 Nguyen, N. C.; Peraire, J.; Cockburn, B. 19 2015 Divergence-conforming HDG methods for Stokes flows. Zbl 1427.76125 Cockburn, Bernardo; Sayas, Francisco-Javier 60 2014 Multigrid for an HDG method. Zbl 1304.65260 Cockburn, B.; Dubois, O.; Gopalakrishnan, J.; Tan, S. 38 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 32 2014 Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation. Zbl 1281.65118 Cockburn, Bernardo; Quenneville-Bélair, Vincent 30 2014 Analysis of variable-degree HDG methods for convection-diffusion equations. II: Semimatching nonconforming meshes. Zbl 1457.65187 Chen, Yanlai; Cockburn, Bernardo 27 2014 Devising \(\mathbf{HDG}\) methods for Stokes flow: an overview. Zbl 1391.76315 Cockburn, Bernardo; Shi, Ke 27 2014 The staggered DG method is the limit of a hybridizable DG method. Zbl 1298.65168 Chung, Eric; Cockburn, Bernardo; Fu, Guosheng 26 2014 Solving convection-diffusion problems on curved domains by extensions from subdomains. Zbl 1304.65246 Cockburn, Bernardo; Solano, Manuel 20 2014 An a posteriori error estimate for the variable-degree Raviart-Thomas method. Zbl 1296.65142 Cockburn, Bernardo; Zhang, Wujun 10 2014 Commuting diagrams for the TNT elements on cubes. Zbl 1290.65109 Cockburn, Bernardo; Qiu, Weifeng 8 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. 52 2013 Superconvergent HDG methods for linear elasticity with weakly symmetric stresses. Zbl 1441.74235 Cockburn, Bernardo; Shi, Ke 43 2013 Analysis of HDG methods for Oseen equations. Zbl 1366.76048 Cesmelioglu, Aycil; Cockburn, Bernardo; Nguyen, Ngoc Cuong; Peraire, Jaume 30 2013 Conditions for superconvergence of HDG methods for Stokes flow. Zbl 1322.65104 Cockburn, Bernardo; Shi, Ke 29 2013 A posteriori error analysis for hybridizable discontinuous Galerkin methods for second-order elliptic problems. Zbl 1277.65089 Cockburn, Bernardo; Zhang, Wujun 26 2013 Space-time hybridizable discontinuous Galerkin method for the advection-diffusion equation on moving and deforming meshes. Zbl 1273.65149 Rhebergen, Sander; Cockburn, Bernardo 10 2013 Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations. Zbl 1269.65086 Cockburn, Bernardo; Merev, Ivan; Qian, Jianliang 1 2013 To CG or to HDG: A comparative study. Zbl 1244.65174 Kirby, Robert M.; Sherwin, Spencer J.; Cockburn, Bernardo 85 2012 Conditions for superconvergence of HDG methods for second-order elliptic problems. Zbl 1251.65158 Cockburn, Bernardo; Qiu, Weifeng; Shi, Ke 63 2012 A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains. Zbl 1426.76298 Rhebergen, Sander; Cockburn, Bernardo 52 2012 Analysis of variable-degree HDG methods for convection-diffusion equations. I: General nonconforming meshes. Zbl 1277.65094 Chen, Yanlai; Cockburn, Bernardo 41 2012 Uniform-in-time superconvergence of HDG methods for the heat equation. Zbl 1251.65138 Chabaud, Brandon; Cockburn, Bernardo 37 2012 A posteriori error estimates for HDG methods. Zbl 1260.65099 Cockburn, Bernardo; Zhang, Wujun 29 2012 Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains. Zbl 1238.65111 Cockburn, Bernardo; Solano, Manuel 29 2012 Superconvergent HDG methods on isoparametric elements for second-order elliptic problems. Zbl 1256.65093 Cockburn, Bernardo; Qiu, Weifeng; Shi, Ke 16 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 15 2012 A projection-based error analysis of HDG methods for Timoshenko beams. Zbl 1427.74163 Celiker, Fatih; Cockburn, Bernardo; Shi, Ke 13 2012 Coupling at a distance HDG and BEM. Zbl 1241.65105 Cockburn, Bernardo; Sayas, Francisco-Javier; Solano, Manuel 11 2012 The devising of symmetric couplings of boundary element and discontinuous Galerkin methods. Zbl 1250.65145 Cockburn, Bernardo; Sayas, Francisco-Javier 9 2012 Coupling of Raviart-Thomas and hybridizable discontinuous Galerkin methods with BEM. Zbl 1260.65101 Cockburn, Bernardo; Guzmán, Johnny; Sayas, Francisco-Javier 9 2012 Divergence-free HDG methods for the vorticity-velocity formulation of the Stokes problem. Zbl 1311.76054 Cockburn, Bernardo; Cui, Jintao 8 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. 145 2011 Analysis of HDG methods for Stokes flow. Zbl 1410.76164 Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Nguyen, Ngoc Cuong; Peraire, Jaume; Sayas, Francisco-Javier 110 2011 High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. Zbl 1364.76093 Nguyen, N. C.; Peraire, J.; Cockburn, B. 82 2011 Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell’s equations. Zbl 1230.78031 Nguyen, N. C.; Peraire, J.; Cockburn, B. 72 2011 Hybridizable discontinuous Galerkin methods. Zbl 1216.65160 Nguyen, N. C.; Peraire, J.; Cockburn, B. 30 2011 Numerical analysis and scientific computing the hybridizable discontinuous Galerkin methods. Zbl 1228.65221 Cockburn, Bernardo 17 2011 A projection-based error analysis of HDG methods. Zbl 1197.65173 Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Sayas, Francisco-Javier 158 2010 A hybridizable discontinuous Galerkin method for Stokes flow. Zbl 1227.76036 Nguyen, N. C.; Peraire, J.; Cockburn, B. 155 2010 A new elasticity element made for enforcing weak stress symmetry. Zbl 1369.74078 Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Guzmán, Johnny 73 2010 A comparison of HDG methods for Stokes flow. Zbl 1203.76079 Cockburn, B.; Nguyen, N. C.; Peraire, J. 39 2010 Boundary-conforming discontinuous Galerkin methods via extensions from subdomains. Zbl 1203.65250 Cockburn, Bernardo; Gupta, Deepa; Reitich, Fernando 16 2010 Hybridizable discontinuous Galerkin methods for Timoshenko beams. Zbl 1203.74078 Celiker, Fatih; Cockburn, Bernardo; Shi, Ke 16 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 14 2010 Hybridization and postprocessing techniques for mixed eigenfunctions. Zbl 1220.65159 Cockburn, B.; Gopalakrishnan, J.; Li, F.; Nguyen, N.-C.; Peraire, J. 11 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 587 2009 Superconvergent discontinuous Galerkin methods for second-order elliptic problems. Zbl 1198.65194 Cockburn, Bernardo; Guzmán, Johnny; Wang, Haiying 108 2009 An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. Zbl 1177.65150 Nguyen, N. C.; Peraire, J.; Cockburn, B. 104 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 102 2009 The derivation of hybridizable discontinuous Galerkin methods for Stokes flow. Zbl 1279.76016 Cockburn, Bernardo; Gopalakrishnan, Jayadeep 71 2009 A hybridizable discontinuous Galerkin method for linear elasticity. Zbl 1176.74196 Soon, S.-C.; Cockburn, B.; Stolarski, Henryk K. 70 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. 40 2009 A hybridizable and superconvergent discontinuous Galerkin method for biharmonic problems. Zbl 1203.65249 Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny 34 2009 An equal-order DG method for the incompressible Navier-Stokes equations. Zbl 1203.76080 Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik 29 2009 Local derivative post-processing for the discontinuous Galerkin method. Zbl 1176.65108 Ryan, Jennifer K.; Cockburn, Bernardo 26 2009 Foreword: Discontinuous Galerkin methods for partial differential equations. Zbl 1203.65005 5 2009 A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. Zbl 1198.65193 Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny 152 2008 An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. Zbl 1187.65110 Nguyen, N. C.; Peraire, J.; Cockburn, B. 147 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 46 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 14 2008 ...and 91 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,381 Authors 169 Shu, Chi-Wang 112 Cockburn, Bernardo 67 Dumbser, Michael 58 Qiu, Jianxian 56 Xu, Yan 48 Baccouch, Mahboub 47 Antonietti, Paola Francesca 41 Ye, Xiu 40 Chung, Tsz Shun Eric 39 Dawson, Clint N. 39 Di Pietro, Daniele Antonio 39 Wang, Zhijian 38 Ern, Alexandre 37 Cheng, Yingda 37 Liu, Tiegang 37 Qiu, Jingmei 34 Xia, Yinhua 33 Li, Fengyan 33 Li, Jichun 33 Xing, Yulong 32 Nguyen, Ngoc Cuong 32 Ryan, Jennifer K. 32 Schötzau, Dominik 32 Zhang, Shangyou 31 Bassi, Francesco 29 van der Vegt, Jaap J. 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