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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//
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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

Publications by Year

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
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
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
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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. W.
29 Yu, Xijun
29 Zhang, Qiang
28 Houston, Paul
28 Liu, Hailiang
28 Rhebergen, Sander
27 Huang, Yunqing
27 Mu, Lin
27 Yang, Yang
26 Burman, Erik
26 Fu, Guosheng
26 Munz, Claus-Dieter
25 Zhang, Zhimin
24 Jameson, Antony
24 Luo, Hong
24 Xu, Kun
23 Gassner, Gregor J.
23 He, Yinnian
23 Hesthaven, Jan S.
23 Zhang, Mengping
22 Adjerid, Slimane
22 Balsara, Dinshaw S.
22 Feng, Minfu
22 Giani, Stefano
22 Rivière, Beatrice M.
22 Wang, Junping
21 Beirão da Veiga, Lourenço
21 Kanschat, Guido
21 Kirby, Robert M. II
21 Marini, Luisa Donatella
21 Nordström, Jan
21 Solano, Manuel E.
20 Crivellini, Andrea
20 Dolejší, Vít
20 Ferrer, Esteban
20 Perugia, Ilaria
20 Scovazzi, Guglielmo
20 Zhang, Yangwen
20 Zhu, Jun
19 Brezzi, Franco
19 Cheng, Jian
19 Gopalakrishnan, Jay
19 Gudi, Thirupathi
19 Huang, Xuehai
19 Li, Ruo
19 Park, Eun-Jae
19 Ruiz-Baier, Ricardo
19 Tishkin, Vladimir Fëdorovich
19 Titi, Edriss Saleh
19 Toro, Eleuterio Francisco
19 Wang, Fei
18 Feistauer, Miloslav
18 Guzmán, Johnny
18 Hu, Jun
18 Karlsen, Kenneth Hvistendahl
18 Kubatko, Ethan J.
18 Qiu, Weifeng
18 Sayas, Francisco-Javier
17 Aizinger, Vadym
17 Georgoulis, Emmanuil H.
17 Guo, Wei
17 Hughes, Thomas J. R.
17 Lanteri, Stéphane
17 Li, Maojun
17 Manzini, Gianmarco
17 Persson, Per-Olof
17 Schöberl, Joachim
17 Verani, Marco
17 Wheeler, Mary Fanett
17 Xiao, Feng
17 Xu, Jinchao
16 Bazilevs, Yuri
16 Bui-Thanh, Tan
16 Castillo, Paul E.
16 Chen, Gang
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86 Numerical Methods for Partial Differential Equations
80 Communications in Computational Physics
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25 Numerical Algorithms
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10 Comptes Rendus. Mathématique. Académie des Sciences, Paris
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5 Acta Mathematicae Applicatae Sinica. English Series
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