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Author ID: cockburn.bernardo Recent zbMATH articles by "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
all top 5

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

Publications by Year

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
910
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
843
1989
The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems. Zbl 0920.65059
Cockburn, Bernardo; Shu, Chi-Wang
782
1998
Runge–Kutta discontinuous Galerkin methods for convection-dominated problems. Zbl 1065.76135
Cockburn, Bernardo; Shu, Chi-Wang
683
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
583
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
574
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
478
2009
The development of discontinuous Galerkin methods. Zbl 0989.76045
Cockburn, Bernardo; Karniadakis, George E.; Shu, Chi-Wang
292
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
247
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
229
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
155
2001
A locally conservative LDG method for the incompressible Navier-Stokes equations. Zbl 1069.76029
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
144
2005
A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. Zbl 1198.65193
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
134
2008
A projection-based error analysis of HDG methods. Zbl 1197.65173
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Sayas, Francisco-Javier
132
2010
An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. Zbl 1187.65110
Nguyen, N. C.; Peraire, J.; Cockburn, B.
125
2008
Discontinuous Galerkin methods for convection-dominated problems. Zbl 0937.76049
Cockburn, Bernardo
122
1999
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations. Zbl 1049.78019
Cockburn, Bernardo; Li, Fengyan; Shu, Chi-Wang
121
2004
Local discontinuous Galerkin methods for the Stokes system. Zbl 1032.65127
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik; Schwab, Christoph
118
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.
116
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
115
2002
A hybridizable discontinuous Galerkin method for Stokes flow. Zbl 1227.76036
Nguyen, N. C.; Peraire, J.; Cockburn, B.
114
2010
A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations. Zbl 1151.76527
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
104
2007
Analysis of HDG methods for Stokes flow. Zbl 1410.76164
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Nguyen, Ngoc Cuong; Peraire, Jaume; Sayas, Francisco-Javier
99
2011
Superconvergent discontinuous Galerkin methods for second-order elliptic problems. Zbl 1198.65194
Cockburn, Bernardo; Guzmán, Johnny; Wang, Haiying
91
2009
An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. Zbl 1177.65150
Nguyen, N. C.; Peraire, J.; Cockburn, B.
89
2009
Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. Zbl 1341.65045
Cockburn, Bernardo; Di Pietro, Daniele A.; Ern, Alexandre
86
2016
Discontinuous Galerkin methods. Zbl 1036.65079
Cockburn, Bernardo
84
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
82
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
81
2003
To CG or to HDG: A comparative study. Zbl 1244.65174
Kirby, Robert M.; Sherwin, Spencer J.; Cockburn, Bernardo
69
2012
Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127
Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella
68
2000
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. Zbl 1364.76093
Nguyen, N. C.; Peraire, J.; Cockburn, B.
66
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
66
2007
A characterization of hybridized mixed methods for second order elliptic problems. Zbl 1084.65113
Cockburn, Bernardo; Gopalakrishnan, Jayadeep
65
2004
Stabilization mechanisms in discontinuous Galerkin finite element methods. Zbl 1125.65102
Brezzi, F.; Cockburn, B.; Marini, L. D.; Süli, E.
60
2006
A new elasticity element made for enforcing weak stress symmetry. Zbl 1369.74078
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Guzmán, Johnny
58
2010
A hybridizable discontinuous Galerkin method for linear elasticity. Zbl 1176.74196
Soon, S.-C.; Cockburn, B.; Stolarski, Henryk K.
57
2009
The derivation of hybridizable discontinuous Galerkin methods for Stokes flow. Zbl 1279.76016
Cockburn, Bernardo; Gopalakrishnan, Jayadeep
57
2009
Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell’s equations. Zbl 1230.78031
Nguyen, N. C.; Peraire, J.; Cockburn, B.
57
2011
Nonlinearly stable compact schemes for shock calculations. Zbl 0805.65085
Cockburn, Bernardo; Shu, Chi-Wang
54
1994
Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24–26, 1999. Zbl 0935.00043
54
2000
A mixed finite element method for elasticity in three dimensions. Zbl 1125.74382
Adams, Scot; Cockburn, Bernardo
54
2005
Conditions for superconvergence of HDG methods for second-order elliptic problems. Zbl 1251.65158
Cockburn, Bernardo; Qiu, Weifeng; Shi, Ke
53
2012
An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems. Zbl 1143.76031
Cockburn, Bernardo; Dong, Bo
52
2007
An introduction to the discontinuous Galerkin method for convection-dominated problems. Zbl 0927.65120
Cockburn, Bernardo
51
1998
Hybridized globally divergence-free LDG methods. I: The Stokes problem. Zbl 1087.76061
Carrero, Jesús; Cockburn, Bernardo; Schötzau, Dominik
51
2006
Divergence-conforming HDG methods for Stokes flows. Zbl 1427.76125
Cockburn, Bernardo; Sayas, Francisco-Javier
49
2014
A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains. Zbl 1426.76298
Rhebergen, Sander; Cockburn, Bernardo
48
2012
The local discontinuous Galerkin method for the Oseen equations. Zbl 1066.76036
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
46
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.
45
2013
Some extensions of the local discontinuous Galerkin method for convection-diffusion equations in multidimensions. Zbl 0960.65107
Cockburn, Bernardo; Dawson, Clint
40
2000
Continuous dependence on the nonlinearities of solutions of degenerate parabolic equations. Zbl 0921.35017
Cockburn, B.; Gripenberg, G.
39
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
39
2008
Incompressible finite elements via hybridization. I: The Stokes system in two space dimensions. Zbl 1145.76402
Cockburn, Bernardo; Gopalakrishnan, Jayadeep
39
2005
Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems. Zbl 0866.35091
Cockburn, Bernardo; Jones, Don A.; Titi, Edriss S.
38
1997
Superconvergent HDG methods for linear elasticity with weakly symmetric stresses. Zbl 1441.74235
Cockburn, Bernardo; Shi, Ke
37
2013
An error estimate for finite volume methods for multidimensional conservation laws. Zbl 0855.65103
Cockburn, Bernardo; Coquel, Frédéric; LeFloch, Philippe
36
1994
Error estimates for finite element methods for scalar conservation laws. Zbl 0861.65077
Cockburn, Bernardo; Gremaud, Pierre-Alain
36
1996
Convergence of the finite volume method for multidimensional conservation laws. Zbl 0845.65051
Cockburn, B.; Coquel, F.; LeFloch, P. G.
35
1995
Analysis of variable-degree HDG methods for convection-diffusion equations. I: General nonconforming meshes. Zbl 1277.65094
Chen, Yanlai; Cockburn, Bernardo
35
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
35
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
33
2005
A comparison of HDG methods for Stokes flow. Zbl 1203.76079
Cockburn, B.; Nguyen, N. C.; Peraire, J.
33
2010
A hybridizable discontinuous Galerkin formulation for non-linear elasticity. Zbl 1423.74895
Kabaria, Hardik; Lew, Adrian J.; Cockburn, Bernardo
33
2015
Discontinuous Galerkin methods for incompressible elastic materials. Zbl 1128.74041
Cockburn, Bernardo; Schötzau, Dominik; Wang, Jing
32
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.
31
2009
The embedded discontinuous Galerkin method: application to linear shell problems. Zbl 1194.74403
Güzey, S.; Cockburn, B.; Stolarski, H. K.
31
2007
Locally conservative fluxes for the continuous Galerkin method. Zbl 1155.65100
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Wang, Haiying
31
2007
High-order RKDG methods for computational electromagnetics. Zbl 1091.78015
Chen, Min-Hung; Cockburn, Bernardo; Reitich, Fernando
30
2005
The local discontinuous Galerkin method for linearized incompressible fluid flow: a review. Zbl 1138.76382
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
30
2005
A hybridizable and superconvergent discontinuous Galerkin method for biharmonic problems. Zbl 1203.65249
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
29
2009
A hybridizable discontinuous Galerkin method for fractional diffusion problems. Zbl 1329.26013
Cockburn, Bernardo; Mustapha, Kassem
29
2015
The local projection \(P^ 0-P^ 1\)-discontinuous-Galerkin finite element method for scalar conservation laws. Zbl 0715.65079
Chavent, Guy; Cockburn, Bernardo
29
1989
Multigrid for an HDG method. Zbl 1304.65260
Cockburn, B.; Dubois, O.; Gopalakrishnan, J.; Tan, S.
29
2014
Uniform-in-time superconvergence of HDG methods for the heat equation. Zbl 1251.65138
Chabaud, Brandon; Cockburn, Bernardo
29
2012
Devising discontinuous Galerkin methods for nonlinear hyperbolic conservation laws. Zbl 0974.65092
Cockburn, Bernardo
28
2001
Error analysis of variable degree mixed methods for elliptic problems via hybridization. Zbl 1078.65093
Cockburn, Bernardo; Gopalakrishnan, Jayadeep
28
2005
Static condensation, hybridization, and the devising of the HDG methods. Zbl 1357.65256
Cockburn, Bernardo
28
2016
Incompressible finite elements via hybridization. II: The Stokes system in three space dimensions. Zbl 1145.76403
Cockburn, Bernardo; Gopalakrishnan, Jayadeep
28
2005
Superconvergence by \(M\)-decompositions. I: General theory for HDG methods for diffusion. Zbl 1361.65084
Cockburn, Bernardo; Fu, Guosheng; Sayas, Francisco Javier
27
2017
Hybridizable discontinuous Galerkin methods. Zbl 1216.65160
Nguyen, N. C.; Peraire, J.; Cockburn, B.
26
2011
Conditions for superconvergence of HDG methods for Stokes flow. Zbl 1322.65104
Cockburn, Bernardo; Shi, Ke
26
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.
26
1998
An equal-order DG method for the incompressible Navier-Stokes equations. Zbl 1203.76080
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
25
2009
Analysis of HDG methods for Oseen equations. Zbl 1366.76048
Cesmelioglu, Aycil; Cockburn, Bernardo; Nguyen, Ngoc Cuong; Peraire, Jaume
25
2013
Devising \(\mathbf{HDG}\) methods for Stokes flow: an overview. Zbl 1391.76315
Cockburn, Bernardo; Shi, Ke
24
2014
Local derivative post-processing for the discontinuous Galerkin method. Zbl 1176.65108
Ryan, Jennifer K.; Cockburn, Bernardo
24
2009
A posteriori error estimates for HDG methods. Zbl 1260.65099
Cockburn, Bernardo; Zhang, Wujun
24
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
24
2014
An explicit hybridizable discontinuous Galerkin method for the acoustic wave equation. Zbl 1423.76280
Stanglmeier, M.; Nguyen, N. C.; Peraire, J.; Cockburn, B.
21
2016
Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode. Zbl 0833.76033
Chen, Zhangxin; Cockburn, Bernardo; Gardner, Carl L.; Jerome, Joseph W.
21
1995
Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation. Zbl 1281.65118
Cockburn, Bernardo; Quenneville-Bélair, Vincent
21
2014
The staggered DG method is the limit of a hybridizable DG method. Zbl 1298.65168
Chung, Eric; Cockburn, Bernardo; Fu, Guosheng
21
2014
Analysis of variable-degree HDG methods for convection-diffusion equations. II: Semimatching nonconforming meshes. Zbl 1457.65187
Chen, Yanlai; Cockburn, Bernardo
20
2014
A posteriori error analysis for hybridizable discontinuous Galerkin methods for second-order elliptic problems. Zbl 1277.65089
Cockburn, Bernardo; Zhang, Wujun
19
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.
19
2015
Locking-free optimal discontinuous Galerkin methods for Timoshenko beams. Zbl 1127.74041
Celiker, Fatih; Cockburn, Bernardo; Stolarski, Henryk K.
19
2006
Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains. Zbl 1238.65111
Cockburn, Bernardo; Solano, Manuel
19
2012
Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems. Zbl 1339.26021
Mustapha, Kassem; Nour, Maher; Cockburn, Bernardo
18
2016
Symplectic Hamiltonian finite element methods for linear elastodynamics. Zbl 07414362
Sánchez, Manuel A.; Cockburn, Bernardo; Nguyen, Ngoc-Cuong; Peraire, Jaime
2
2021
Interpolatory HDG method for parabolic semilinear PDEs. Zbl 1422.65252
Cockburn, Bernardo; Singler, John R.; Zhang, Yangwen
12
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
7
2019
An algorithm for stabilizing hybridizable discontinuous Galerkin methods for nonlinear elasticity. Zbl 1451.74205
Cockburn, Bernardo; Shen, Jiguang
2
2019
Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by \(M\)-decompositions. Zbl 1477.65205
Cockburn, Bernardo; Fu, Guosheng
17
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
11
2018
An introduction to the theory of \(M\)-decompositions. Zbl 1416.65412
Cockburn, Bernardo; Fu, Guosheng; Shi, Ke
1
2018
Supercloseness of primal-dual Galerkin approximations for second order elliptic problems. Zbl 1398.65294
Cockburn, Bernardo; Sánchez, Manuel A.; Xiong, Chunguang
1
2018
Discrete \(H^1\)-inequalities for spaces admitting M-decompositions. Zbl 1407.65285
Cockburn, Bernardo; Fu, Guosheng; Qiu, Weifeng
1
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
35
2017
Superconvergence by \(M\)-decompositions. I: General theory for HDG methods for diffusion. Zbl 1361.65084
Cockburn, Bernardo; Fu, Guosheng; Sayas, Francisco Javier
27
2017
Superconvergence by \(M\)-decompositions. III: Construction of three-dimensional finite elements. Zbl 1412.65137
Cockburn, Bernardo; Fu, Guosheng
17
2017
Superconvergence by \(M\)-decompositions. II: Construction of two-dimensional finite elements. Zbl 1412.65205
Cockburn, Bernardo; Fu, Guosheng
16
2017
Symplectic Hamiltonian HDG methods for wave propagation phenomena. Zbl 1380.65421
Sánchez, M. A.; Ciuca, C.; Nguyen, N. C.; Peraire, J.; Cockburn, B.
13
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
13
2017
A systematic construction of finite element commuting exact sequences. Zbl 1369.65145
Cockburn, Bernardo; Fu, Guosheng
10
2017
Adjoint-based, superconvergent Galerkin approximations of linear functionals. Zbl 1382.35097
Cockburn, Bernardo; Wang, Zhu
6
2017
Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. Zbl 1341.65045
Cockburn, Bernardo; Di Pietro, Daniele A.; Ern, Alexandre
86
2016
Static condensation, hybridization, and the devising of the HDG methods. Zbl 1357.65256
Cockburn, Bernardo
28
2016
An explicit hybridizable discontinuous Galerkin method for the acoustic wave equation. Zbl 1423.76280
Stanglmeier, M.; Nguyen, N. C.; Peraire, J.; Cockburn, B.
21
2016
Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems. Zbl 1339.26021
Mustapha, Kassem; Nour, Maher; Cockburn, Bernardo
18
2016
A hybridizable discontinuous Galerkin method for the \(p\)-Laplacian. Zbl 1382.65383
Cockburn, Bernardo; Shen, Jiguang
16
2016
Superconvergent HDG methods for linear, stationary, third-order equations in one-space dimension. Zbl 1344.65070
Chen, Yanlai; Cockburn, Bernardo; Dong, Bo
13
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
8
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
7
2016
Contraction property of adaptive hybridizable discontinuous Galerkin methods. Zbl 1332.65164
Cockburn, Bernardo; Nochetto, Ricardo H.; Zhang, Wujun
5
2016
Hybridizable discontinuous Galerkin and mixed finite element methods for elliptic problems on surfaces. Zbl 1416.65439
Cockburn, Bernardo; Demlow, Alan
3
2016
A hybridizable discontinuous Galerkin formulation for non-linear elasticity. Zbl 1423.74895
Kabaria, Hardik; Lew, Adrian J.; Cockburn, Bernardo
33
2015
A hybridizable discontinuous Galerkin method for fractional diffusion problems. Zbl 1329.26013
Cockburn, Bernardo; Mustapha, Kassem
29
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.
19
2015
Analysis of an HDG method for linear elasticity. Zbl 1352.74037
Fu, Guosheng; Cockburn, B.; Stolarski, H.
16
2015
A class of embedded discontinuous Galerkin methods for computational fluid dynamics. Zbl 1349.76245
Nguyen, N. C.; Peraire, J.; Cockburn, B.
14
2015
Divergence-conforming HDG methods for Stokes flows. Zbl 1427.76125
Cockburn, Bernardo; Sayas, Francisco-Javier
49
2014
Multigrid for an HDG method. Zbl 1304.65260
Cockburn, B.; Dubois, O.; Gopalakrishnan, J.; Tan, S.
29
2014
Devising \(\mathbf{HDG}\) methods for Stokes flow: an overview. Zbl 1391.76315
Cockburn, Bernardo; Shi, Ke
24
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
24
2014
Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation. Zbl 1281.65118
Cockburn, Bernardo; Quenneville-Bélair, Vincent
21
2014
The staggered DG method is the limit of a hybridizable DG method. Zbl 1298.65168
Chung, Eric; Cockburn, Bernardo; Fu, Guosheng
21
2014
Analysis of variable-degree HDG methods for convection-diffusion equations. II: Semimatching nonconforming meshes. Zbl 1457.65187
Chen, Yanlai; Cockburn, Bernardo
20
2014
Solving convection-diffusion problems on curved domains by extensions from subdomains. Zbl 1304.65246
Cockburn, Bernardo; Solano, Manuel
15
2014
An a posteriori error estimate for the variable-degree Raviart-Thomas method. Zbl 1296.65142
Cockburn, Bernardo; Zhang, Wujun
8
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.
45
2013
Superconvergent HDG methods for linear elasticity with weakly symmetric stresses. Zbl 1441.74235
Cockburn, Bernardo; Shi, Ke
37
2013
Conditions for superconvergence of HDG methods for Stokes flow. Zbl 1322.65104
Cockburn, Bernardo; Shi, Ke
26
2013
Analysis of HDG methods for Oseen equations. Zbl 1366.76048
Cesmelioglu, Aycil; Cockburn, Bernardo; Nguyen, Ngoc Cuong; Peraire, Jaume
25
2013
A posteriori error analysis for hybridizable discontinuous Galerkin methods for second-order elliptic problems. Zbl 1277.65089
Cockburn, Bernardo; Zhang, Wujun
19
2013
Space-time hybridizable discontinuous Galerkin method for the advection-diffusion equation on moving and deforming meshes. Zbl 1273.65149
Rhebergen, Sander; Cockburn, Bernardo
9
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
69
2012
Conditions for superconvergence of HDG methods for second-order elliptic problems. Zbl 1251.65158
Cockburn, Bernardo; Qiu, Weifeng; Shi, Ke
53
2012
A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains. Zbl 1426.76298
Rhebergen, Sander; Cockburn, Bernardo
48
2012
Analysis of variable-degree HDG methods for convection-diffusion equations. I: General nonconforming meshes. Zbl 1277.65094
Chen, Yanlai; Cockburn, Bernardo
35
2012
Uniform-in-time superconvergence of HDG methods for the heat equation. Zbl 1251.65138
Chabaud, Brandon; Cockburn, Bernardo
29
2012
A posteriori error estimates for HDG methods. Zbl 1260.65099
Cockburn, Bernardo; Zhang, Wujun
24
2012
Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains. Zbl 1238.65111
Cockburn, Bernardo; Solano, Manuel
19
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
14
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
9
2012
The devising of symmetric couplings of boundary element and discontinuous Galerkin methods. Zbl 1250.65145
Cockburn, Bernardo; Sayas, Francisco-Javier
7
2012
Coupling of Raviart-Thomas and hybridizable discontinuous Galerkin methods with BEM. Zbl 1260.65101
Cockburn, Bernardo; Guzmán, Johnny; Sayas, Francisco-Javier
7
2012
Divergence-free HDG methods for the vorticity-velocity formulation of the Stokes problem. Zbl 1311.76054
Cockburn, Bernardo; Cui, Jintao
6
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.
116
2011
Analysis of HDG methods for Stokes flow. Zbl 1410.76164
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Nguyen, Ngoc Cuong; Peraire, Jaume; Sayas, Francisco-Javier
99
2011
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. Zbl 1364.76093
Nguyen, N. C.; Peraire, J.; Cockburn, B.
66
2011
Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell’s equations. Zbl 1230.78031
Nguyen, N. C.; Peraire, J.; Cockburn, B.
57
2011
Hybridizable discontinuous Galerkin methods. Zbl 1216.65160
Nguyen, N. C.; Peraire, J.; Cockburn, B.
26
2011
Numerical analysis and scientific computing the hybridizable discontinuous Galerkin methods. Zbl 1228.65221
Cockburn, Bernardo
13
2011
A projection-based error analysis of HDG methods. Zbl 1197.65173
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Sayas, Francisco-Javier
132
2010
A hybridizable discontinuous Galerkin method for Stokes flow. Zbl 1227.76036
Nguyen, N. C.; Peraire, J.; Cockburn, B.
114
2010
A new elasticity element made for enforcing weak stress symmetry. Zbl 1369.74078
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Guzmán, Johnny
58
2010
A comparison of HDG methods for Stokes flow. Zbl 1203.76079
Cockburn, B.; Nguyen, N. C.; Peraire, J.
33
2010
Hybridizable discontinuous Galerkin methods for Timoshenko beams. Zbl 1203.74078
Celiker, Fatih; Cockburn, Bernardo; Shi, Ke
16
2010
Boundary-conforming discontinuous Galerkin methods via extensions from subdomains. Zbl 1203.65250
Cockburn, Bernardo; Gupta, Deepa; Reitich, Fernando
15
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
11
2010
Hybridization and postprocessing techniques for mixed eigenfunctions. Zbl 1220.65159
Cockburn, B.; Gopalakrishnan, J.; Li, F.; Nguyen, N.-C.; Peraire, J.
8
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
478
2009
Superconvergent discontinuous Galerkin methods for second-order elliptic problems. Zbl 1198.65194
Cockburn, Bernardo; Guzmán, Johnny; Wang, Haiying
91
2009
An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. Zbl 1177.65150
Nguyen, N. C.; Peraire, J.; Cockburn, B.
89
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
82
2009
A hybridizable discontinuous Galerkin method for linear elasticity. Zbl 1176.74196
Soon, S.-C.; Cockburn, B.; Stolarski, Henryk K.
57
2009
The derivation of hybridizable discontinuous Galerkin methods for Stokes flow. Zbl 1279.76016
Cockburn, Bernardo; Gopalakrishnan, Jayadeep
57
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.
31
2009
A hybridizable and superconvergent discontinuous Galerkin method for biharmonic problems. Zbl 1203.65249
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
29
2009
An equal-order DG method for the incompressible Navier-Stokes equations. Zbl 1203.76080
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
25
2009
Local derivative post-processing for the discontinuous Galerkin method. Zbl 1176.65108
Ryan, Jennifer K.; Cockburn, Bernardo
24
2009
Foreword: Discontinuous Galerkin methods for partial differential equations. Zbl 1203.65005
4
2009
A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. Zbl 1198.65193
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
134
2008
An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. Zbl 1187.65110
Nguyen, N. C.; Peraire, J.; Cockburn, B.
125
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
39
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
12
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
1
2008
A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations. Zbl 1151.76527
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
104
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
66
2007
An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems. Zbl 1143.76031
Cockburn, Bernardo; Dong, Bo
52
2007
The embedded discontinuous Galerkin method: application to linear shell problems. Zbl 1194.74403
Güzey, S.; Cockburn, B.; Stolarski, H. K.
31
2007
Locally conservative fluxes for the continuous Galerkin method. Zbl 1155.65100
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Wang, Haiying
31
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
3
2007
Adjoint recovery of superconvergent linear functionals from Galerkin approximations. The one-dimensional case. Zbl 1134.65052
Cockburn, Bernardo; Ichikawa, Ryuhei
2
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
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821 Journal of Computational Physics
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14 BIT
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10 Comptes Rendus. Mathématique. Académie des Sciences, Paris
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4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
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