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Cockburn, Bernardo

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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: 188 Publications since 1980, including 2 Books
Biographic References: 1 Publication
all top 5

Co-Authors

13 single-authored
16 Shu, Chi-Wang
15 Nguyen, Ngoc Cuong
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
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 Sánchez, Manuel A.
3 Süli, Endre E.
3 Wang, Haiying
2 Albert, Samuel
2 Arnold, Douglas Norman
2 Çeşmelioğlu, Ayçıl
2 Chavent, Guy
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, Jaume
2 Peterson, Todd E.
2 Schwab, Christoph
2 Shen, Jiguang
2 Singler, John R.
2 Titi, Edriss Saleh
2 Triandaf, Ioana
2 Yang, Jimmy Xiangrong
2 Yenikaya, Bayram
2 Zhang, Yangwen
1 Adams, Scot
1 Aizinger, Vadym
1 Bamberger, Alain
1 Bourgeat, Alain P.
1 Bustinza, Rommel A.
1 Carrero, Jesús
1 Chabaud, Brandon M.
1 Chen, Gang
1 Chen, Min-Hung
1 Ciuca, C.
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 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 Lazarov, Raytcho D.
1 Lew, Adrian J.
1 Lin, Sanyih
1 Merev, Ivan
1 Nochetto, Ricardo Horacio
1 Nour, Maher
1 Quarteroni, Alfio M.
1 Quenneville-Bélair, Vincent
1 Restelli, Marco
1 Ryan, Jennifer K.
1 Sacco, Riccardo
1 Sherwin, Spencer J.
1 Soon, See-Chew
1 Soon, Sew-Chew
1 Stanglmeier, M.
...and 7 more Co-Authors

Publications by Year

Citations contained in zbMATH Open

176 Publications have been cited 10,672 times in 3,874 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
781
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
725
1989
The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems. Zbl 0920.65059
Cockburn, Bernardo; Shu, Chi-Wang
661
1998
Runge–Kutta discontinuous Galerkin methods for convection-dominated problems. Zbl 1065.76135
Cockburn, Bernardo; Shu, Chi-Wang
607
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
509
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
507
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
404
2009
The development of discontinuous Galerkin methods. Zbl 0989.76045
Cockburn, Bernardo; Karniadakis, George E.; Shu, Chi-Wang
259
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
215
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
205
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
135
2001
A locally conservative LDG method for the incompressible Navier-Stokes equations. Zbl 1069.76029
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
130
2005
A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. Zbl 1198.65193
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
118
2008
A projection-based error analysis of HDG methods. Zbl 1197.65173
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Sayas, Francisco-Javier
117
2010
Discontinuous Galerkin methods for convection-dominated problems. Zbl 0937.76049
Cockburn, Bernardo
111
1999
An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. Zbl 1187.65110
Nguyen, N. C.; Peraire, J.; Cockburn, B.
109
2008
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations. Zbl 1049.78019
Cockburn, Bernardo; Li, Fengyan; Shu, Chi-Wang
106
2004
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
103
2002
Local discontinuous Galerkin methods for the Stokes system. Zbl 1032.65127
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik; Schwab, Christoph
103
2002
A hybridizable discontinuous Galerkin method for Stokes flow. Zbl 1227.76036
Nguyen, N. C.; Peraire, J.; Cockburn, B.
100
2010
An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. Zbl 1391.76353
Nguyen, N. C.; Peraire, J.; Cockburn, B.
97
2011
Analysis of HDG methods for Stokes flow. Zbl 1410.76164
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Nguyen, Ngoc Cuong; Peraire, Jaume; Sayas, Francisco-Javier
91
2011
A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations. Zbl 1151.76527
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
89
2007
An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. Zbl 1177.65150
Nguyen, N. C.; Peraire, J.; Cockburn, B.
80
2009
Superconvergent discontinuous Galerkin methods for second-order elliptic problems. Zbl 1198.65194
Cockburn, Bernardo; Guzmán, Johnny; Wang, Haiying
80
2009
Discontinuous Galerkin methods. Zbl 1036.65079
Cockburn, Bernardo
77
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
72
2009
Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. Zbl 1341.65045
Cockburn, Bernardo; Di Pietro, Daniele A.; Ern, Alexandre
69
2016
Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Zbl 1015.65049
Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre
66
2003
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
Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127
Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella
64
2000
To CG or to HDG: A comparative study. Zbl 1244.65174
Kirby, Robert M.; Sherwin, Spencer J.; Cockburn, Bernardo
60
2012
Stabilization mechanisms in discontinuous Galerkin finite element methods. Zbl 1125.65102
Brezzi, F.; Cockburn, B.; Marini, L. D.; Süli, E.
57
2006
A characterization of hybridized mixed methods for second order elliptic problems. Zbl 1084.65113
Cockburn, Bernardo; Gopalakrishnan, Jayadeep
55
2004
Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24–26, 1999. Zbl 0935.00043
Cockburn, Bernardo (ed.); Karniadakis, George E. (ed.); Shu, Chi-Wang (ed.)
53
2000
Nonlinearly stable compact schemes for shock calculations. Zbl 0805.65085
Cockburn, Bernardo; Shu, Chi-Wang
53
1994
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. Zbl 1364.76093
Nguyen, N. C.; Peraire, J.; Cockburn, B.
53
2011
A new elasticity element made for enforcing weak stress symmetry. Zbl 1369.74078
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Guzmán, Johnny
52
2010
The derivation of hybridizable discontinuous Galerkin methods for Stokes flow. Zbl 1279.76016
Cockburn, Bernardo; Gopalakrishnan, Jayadeep
51
2009
An introduction to the discontinuous Galerkin method for convection-dominated problems. Zbl 0927.65120
Cockburn, Bernardo
48
1998
A hybridizable discontinuous Galerkin method for linear elasticity. Zbl 1176.74196
Soon, S.-C.; Cockburn, B.; Stolarski, Henryk K.
48
2009
Conditions for superconvergence of HDG methods for second-order elliptic problems. Zbl 1251.65158
Cockburn, Bernardo; Qiu, Weifeng; Shi, Ke
48
2012
A mixed finite element method for elasticity in three dimensions. Zbl 1125.74382
Adams, Scot; Cockburn, Bernardo
47
2005
Hybridized globally divergence-free LDG methods. I: The Stokes problem. Zbl 1087.76061
Carrero, Jesús; Cockburn, Bernardo; Schötzau, Dominik
46
2006
Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell’s equations. Zbl 1230.78031
Nguyen, N. C.; Peraire, J.; Cockburn, B.
46
2011
An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems. Zbl 1143.76031
Cockburn, Bernardo; Dong, Bo
45
2007
The local discontinuous Galerkin method for the Oseen equations. Zbl 1066.76036
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
43
2004
Divergence-conforming HDG methods for Stokes flows. Zbl 1427.76125
Cockburn, Bernardo; Sayas, Francisco-Javier
43
2014
A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains. Zbl 1426.76298
Rhebergen, Sander; Cockburn, Bernardo
42
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.
39
2013
Some extensions of the local discontinuous Galerkin method for convection-diffusion equations in multidimensions. Zbl 0960.65107
Cockburn, Bernardo; Dawson, Clint
38
2000
Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems. Zbl 0866.35091
Cockburn, Bernardo; Jones, Don A.; Titi, Edriss S.
36
1997
Error estimates for finite element methods for scalar conservation laws. Zbl 0861.65077
Cockburn, Bernardo; Gremaud, Pierre-Alain
36
1996
Optimal convergence of the original DG method for the transport-reaction equation on special meshes. Zbl 1168.65058
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
35
2008
Convergence of the finite volume method for multidimensional conservation laws. Zbl 0845.65051
Cockburn, B.; Coquel, F.; LeFloch, P. G.
35
1995
An error estimate for finite volume methods for multidimensional conservation laws. Zbl 0855.65103
Cockburn, Bernardo; Coquel, Frédéric; LeFloch, Philippe
35
1994
Continuous dependence on the nonlinearities of solutions of degenerate parabolic equations. Zbl 0921.35017
Cockburn, B.; Gripenberg, G.
34
1999
Incompressible finite elements via hybridization. I: The Stokes system in two space dimensions. Zbl 1145.76402
Cockburn, Bernardo; Gopalakrishnan, Jayadeep
34
2005
Superconvergent HDG methods for linear elasticity with weakly symmetric stresses. Zbl 1441.74235
Cockburn, Bernardo; Shi, Ke
30
2013
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
30
2005
Locally conservative fluxes for the continuous Galerkin method. Zbl 1155.65100
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Wang, Haiying
29
2007
The embedded discontinuous Galerkin method: application to linear shell problems. Zbl 1194.74403
Güzey, S.; Cockburn, B.; Stolarski, H. K.
29
2007
High-order RKDG methods for computational electromagnetics. Zbl 1091.78015
Chen, Min-Hung; Cockburn, Bernardo; Reitich, Fernando
29
2005
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.
29
2009
Analysis of variable-degree HDG methods for convection-diffusion equations. I: General nonconforming meshes. Zbl 1277.65094
Chen, Yanlai; Cockburn, Bernardo
29
2012
The local discontinuous Galerkin method for linearized incompressible fluid flow: a review. Zbl 1138.76382
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
29
2005
Discontinuous Galerkin methods for incompressible elastic materials. Zbl 1128.74041
Cockburn, Bernardo; Schötzau, Dominik; Wang, Jing
29
2006
A hybridizable discontinuous Galerkin method for fractional diffusion problems. Zbl 1329.26013
Cockburn, Bernardo; Mustapha, Kassem
27
2015
Incompressible finite elements via hybridization. II: The Stokes system in three space dimensions. Zbl 1145.76403
Cockburn, Bernardo; Gopalakrishnan, Jayadeep
27
2005
A comparison of HDG methods for Stokes flow. Zbl 1203.76079
Cockburn, B.; Nguyen, N. C.; Peraire, J.
27
2010
Error analysis of variable degree mixed methods for elliptic problems via hybridization. Zbl 1078.65093
Cockburn, Bernardo; Gopalakrishnan, Jayadeep
26
2005
A hybridizable discontinuous Galerkin formulation for non-linear elasticity. Zbl 1423.74895
Kabaria, Hardik; Lew, Adrian J.; Cockburn, Bernardo
25
2015
Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations. Zbl 1422.65377
Cesmelioglu, Aycil; Cockburn, Bernardo; Qiu, Weifeng
25
2017
The local projection \(P^ 0-P^ 1\)-discontinuous-Galerkin finite element method for scalar conservation laws. Zbl 0715.65079
Chavent, Guy; Cockburn, Bernardo
25
1989
Conditions for superconvergence of HDG methods for Stokes flow. Zbl 1322.65104
Cockburn, Bernardo; Shi, Ke
25
2013
A hybridizable and superconvergent discontinuous Galerkin method for biharmonic problems. Zbl 1203.65249
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
25
2009
Devising discontinuous Galerkin methods for nonlinear hyperbolic conservation laws. Zbl 0974.65092
Cockburn, Bernardo
24
2001
Uniform-in-time superconvergence of HDG methods for the heat equation. Zbl 1251.65138
Chabaud, Brandon; Cockburn, Bernardo
24
2012
Hybridizable discontinuous Galerkin methods. Zbl 1216.65160
Nguyen, N. C.; Peraire, J.; Cockburn, B.
24
2011
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
Quarteroni, Alfio (ed.); Cockburn, B.; Johnson, C.; Shu, C.-W.; Tadmor, E.
23
1998
Devising \(\mathbf{HDG}\) methods for Stokes flow: an overview. Zbl 1391.76315
Cockburn, Bernardo; Shi, Ke
22
2014
An equal-order DG method for the incompressible Navier-Stokes equations. Zbl 1203.76080
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
22
2009
Static condensation, hybridization, and the devising of the HDG methods. Zbl 1357.65256
Cockburn, Bernardo
21
2016
Superconvergence by \(M\)-decompositions. I: General theory for HDG methods for diffusion. Zbl 1361.65084
Cockburn, Bernardo; Fu, Guosheng; Sayas, Francisco Javier
21
2017
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
Multigrid for an HDG method. Zbl 1304.65260
Cockburn, B.; Dubois, O.; Gopalakrishnan, J.; Tan, S.
21
2014
A posteriori error estimates for HDG methods. Zbl 1260.65099
Cockburn, Bernardo; Zhang, Wujun
20
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
20
2014
Analysis of HDG methods for Oseen equations. Zbl 1366.76048
Cesmelioglu, Aycil; Cockburn, Bernardo; Nguyen, Ngoc Cuong; Peraire, Jaume
19
2013
Local derivative post-processing for the discontinuous Galerkin method. Zbl 1176.65108
Ryan, Jennifer K.; Cockburn, Bernardo
18
2009
Locking-free optimal discontinuous Galerkin methods for Timoshenko beams. Zbl 1127.74041
Celiker, Fatih; Cockburn, Bernardo; Stolarski, Henryk K.
18
2006
A priori error estimates for numerical methods for scalar conservation laws. I: The general approach. Zbl 0848.65067
Cockburn, Bernardo; Gremaud, Pierre-Alain
17
1996
Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation. Zbl 1281.65118
Cockburn, Bernardo; Quenneville-Bélair, Vincent
17
2014
Analysis of variable-degree HDG methods for convection-diffusion equations. II: Semimatching nonconforming meshes. Zbl 1457.65187
Chen, Yanlai; Cockburn, Bernardo
17
2014
The staggered DG method is the limit of a hybridizable DG method. Zbl 1298.65168
Chung, Eric; Cockburn, Bernardo; Fu, Guosheng
17
2014
Approximation of the velocity by coupling discontinuous Galerkin and mixed finite element methods for flow problems. Zbl 1023.76020
Cockburn, Bernardo; Dawson, Clint
16
2002
A posteriori error analysis for hybridizable discontinuous Galerkin methods for second-order elliptic problems. Zbl 1277.65089
Cockburn, Bernardo; Zhang, Wujun
16
2013
Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems. Zbl 1339.26021
Mustapha, Kassem; Nour, Maher; Cockburn, Bernardo
16
2016
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.
15
2015
Interpolatory HDG method for parabolic semilinear PDEs. Zbl 1422.65252
Cockburn, Bernardo; Singler, John R.; Zhang, Yangwen
5
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
4
2019
Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by \(M\)-decompositions. Zbl 06983825
Cockburn, Bernardo; Fu, Guosheng
10
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
6
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
25
2017
Superconvergence by \(M\)-decompositions. I: General theory for HDG methods for diffusion. Zbl 1361.65084
Cockburn, Bernardo; Fu, Guosheng; Sayas, Francisco Javier
21
2017
Superconvergence by \(M\)-decompositions. III: Construction of three-dimensional finite elements. Zbl 1412.65137
Cockburn, Bernardo; Fu, Guosheng
14
2017
Superconvergence by \(M\)-decompositions. II: Construction of two-dimensional finite elements. Zbl 1412.65205
Cockburn, Bernardo; Fu, Guosheng
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
10
2017
Symplectic Hamiltonian HDG methods for wave propagation phenomena. Zbl 1380.65421
Sánchez, M. A.; Ciuca, C.; Nguyen, N. C.; Peraire, J.; Cockburn, B.
6
2017
A systematic construction of finite element commuting exact sequences. Zbl 1369.65145
Cockburn, Bernardo; Fu, Guosheng
6
2017
Adjoint-based, superconvergent Galerkin approximations of linear functionals. Zbl 1382.35097
Cockburn, Bernardo; Wang, Zhu
1
2017
Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. Zbl 1341.65045
Cockburn, Bernardo; Di Pietro, Daniele A.; Ern, Alexandre
69
2016
Static condensation, hybridization, and the devising of the HDG methods. Zbl 1357.65256
Cockburn, Bernardo
21
2016
Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems. Zbl 1339.26021
Mustapha, Kassem; Nour, Maher; Cockburn, Bernardo
16
2016
An explicit hybridizable discontinuous Galerkin method for the acoustic wave equation. Zbl 1423.76280
Stanglmeier, M.; Nguyen, N. C.; Peraire, J.; Cockburn, B.
14
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
A hybridizable discontinuous Galerkin method for the \(p\)-Laplacian. Zbl 1382.65383
Cockburn, Bernardo; Shen, Jiguang
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
6
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 method for fractional diffusion problems. Zbl 1329.26013
Cockburn, Bernardo; Mustapha, Kassem
27
2015
A hybridizable discontinuous Galerkin formulation for non-linear elasticity. Zbl 1423.74895
Kabaria, Hardik; Lew, Adrian J.; Cockburn, Bernardo
25
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.
15
2015
Analysis of an HDG method for linear elasticity. Zbl 1352.74037
Fu, Guosheng; Cockburn, B.; Stolarski, H.
12
2015
A class of embedded discontinuous Galerkin methods for computational fluid dynamics. Zbl 1349.76245
Nguyen, N. C.; Peraire, J.; Cockburn, B.
9
2015
Divergence-conforming HDG methods for Stokes flows. Zbl 1427.76125
Cockburn, Bernardo; Sayas, Francisco-Javier
43
2014
Devising \(\mathbf{HDG}\) methods for Stokes flow: an overview. Zbl 1391.76315
Cockburn, Bernardo; Shi, Ke
22
2014
Multigrid for an HDG method. Zbl 1304.65260
Cockburn, B.; Dubois, O.; Gopalakrishnan, J.; Tan, S.
21
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
20
2014
Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation. Zbl 1281.65118
Cockburn, Bernardo; Quenneville-Bélair, Vincent
17
2014
Analysis of variable-degree HDG methods for convection-diffusion equations. II: Semimatching nonconforming meshes. Zbl 1457.65187
Chen, Yanlai; Cockburn, Bernardo
17
2014
The staggered DG method is the limit of a hybridizable DG method. Zbl 1298.65168
Chung, Eric; Cockburn, Bernardo; Fu, Guosheng
17
2014
Solving convection-diffusion problems on curved domains by extensions from subdomains. Zbl 1304.65246
Cockburn, Bernardo; Solano, Manuel
14
2014
An a posteriori error estimate for the variable-degree Raviart-Thomas method. Zbl 1296.65142
Cockburn, Bernardo; Zhang, Wujun
7
2014
Commuting diagrams for the TNT elements on cubes. Zbl 1290.65109
Cockburn, Bernardo; Qiu, Weifeng
7
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.
39
2013
Superconvergent HDG methods for linear elasticity with weakly symmetric stresses. Zbl 1441.74235
Cockburn, Bernardo; Shi, Ke
30
2013
Conditions for superconvergence of HDG methods for Stokes flow. Zbl 1322.65104
Cockburn, Bernardo; Shi, Ke
25
2013
Analysis of HDG methods for Oseen equations. Zbl 1366.76048
Cesmelioglu, Aycil; Cockburn, Bernardo; Nguyen, Ngoc Cuong; Peraire, Jaume
19
2013
A posteriori error analysis for hybridizable discontinuous Galerkin methods for second-order elliptic problems. Zbl 1277.65089
Cockburn, Bernardo; Zhang, Wujun
16
2013
Space-time hybridizable discontinuous Galerkin method for the advection-diffusion equation on moving and deforming meshes. Zbl 1273.65149
Rhebergen, Sander; Cockburn, Bernardo
8
2013
To CG or to HDG: A comparative study. Zbl 1244.65174
Kirby, Robert M.; Sherwin, Spencer J.; Cockburn, Bernardo
60
2012
Conditions for superconvergence of HDG methods for second-order elliptic problems. Zbl 1251.65158
Cockburn, Bernardo; Qiu, Weifeng; Shi, Ke
48
2012
A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains. Zbl 1426.76298
Rhebergen, Sander; Cockburn, Bernardo
42
2012
Analysis of variable-degree HDG methods for convection-diffusion equations. I: General nonconforming meshes. Zbl 1277.65094
Chen, Yanlai; Cockburn, Bernardo
29
2012
Uniform-in-time superconvergence of HDG methods for the heat equation. Zbl 1251.65138
Chabaud, Brandon; Cockburn, Bernardo
24
2012
A posteriori error estimates for HDG methods. Zbl 1260.65099
Cockburn, Bernardo; Zhang, Wujun
20
2012
Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains. Zbl 1238.65111
Cockburn, Bernardo; Solano, Manuel
15
2012
Superconvergent HDG methods on isoparametric elements for second-order elliptic problems. Zbl 1256.65093
Cockburn, Bernardo; Qiu, Weifeng; Shi, Ke
15
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
13
2012
A projection-based error analysis of HDG methods for Timoshenko beams. Zbl 1427.74163
Celiker, Fatih; Cockburn, Bernardo; Shi, Ke
11
2012
Coupling at a distance HDG and BEM. Zbl 1241.65105
Cockburn, Bernardo; Sayas, Francisco-Javier; Solano, Manuel
7
2012
Divergence-free HDG methods for the vorticity-velocity formulation of the Stokes problem. Zbl 1311.76054
Cockburn, Bernardo; Cui, Jintao
6
2012
The devising of symmetric couplings of boundary element and discontinuous Galerkin methods. Zbl 1250.65145
Cockburn, Bernardo; Sayas, Francisco-Javier
5
2012
Coupling of Raviart-Thomas and hybridizable discontinuous Galerkin methods with BEM. Zbl 1260.65101
Cockburn, Bernardo; Guzmán, Johnny; Sayas, Francisco-Javier
4
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.
97
2011
Analysis of HDG methods for Stokes flow. Zbl 1410.76164
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Nguyen, Ngoc Cuong; Peraire, Jaume; Sayas, Francisco-Javier
91
2011
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. Zbl 1364.76093
Nguyen, N. C.; Peraire, J.; Cockburn, B.
53
2011
Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell’s equations. Zbl 1230.78031
Nguyen, N. C.; Peraire, J.; Cockburn, B.
46
2011
Hybridizable discontinuous Galerkin methods. Zbl 1216.65160
Nguyen, N. C.; Peraire, J.; Cockburn, B.
24
2011
Numerical analysis and scientific computing the hybridizable discontinuous Galerkin methods. Zbl 1228.65221
Cockburn, Bernardo
9
2011
A projection-based error analysis of HDG methods. Zbl 1197.65173
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Sayas, Francisco-Javier
117
2010
A hybridizable discontinuous Galerkin method for Stokes flow. Zbl 1227.76036
Nguyen, N. C.; Peraire, J.; Cockburn, B.
100
2010
A new elasticity element made for enforcing weak stress symmetry. Zbl 1369.74078
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Guzmán, Johnny
52
2010
A comparison of HDG methods for Stokes flow. Zbl 1203.76079
Cockburn, B.; Nguyen, N. C.; Peraire, J.
27
2010
Hybridizable discontinuous Galerkin methods for Timoshenko beams. Zbl 1203.74078
Celiker, Fatih; Cockburn, Bernardo; Shi, Ke
14
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
Boundary-conforming discontinuous Galerkin methods via extensions from subdomains. Zbl 1203.65250
Cockburn, Bernardo; Gupta, Deepa; Reitich, Fernando
11
2010
Hybridization and postprocessing techniques for mixed eigenfunctions. Zbl 1220.65159
Cockburn, B.; Gopalakrishnan, J.; Li, F.; Nguyen, N.-C.; Peraire, J.
6
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
404
2009
An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. Zbl 1177.65150
Nguyen, N. C.; Peraire, J.; Cockburn, B.
80
2009
Superconvergent discontinuous Galerkin methods for second-order elliptic problems. Zbl 1198.65194
Cockburn, Bernardo; Guzmán, Johnny; Wang, Haiying
80
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
72
2009
The derivation of hybridizable discontinuous Galerkin methods for Stokes flow. Zbl 1279.76016
Cockburn, Bernardo; Gopalakrishnan, Jayadeep
51
2009
A hybridizable discontinuous Galerkin method for linear elasticity. Zbl 1176.74196
Soon, S.-C.; Cockburn, B.; Stolarski, Henryk K.
48
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.
29
2009
A hybridizable and superconvergent discontinuous Galerkin method for biharmonic problems. Zbl 1203.65249
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
25
2009
An equal-order DG method for the incompressible Navier-Stokes equations. Zbl 1203.76080
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
22
2009
Local derivative post-processing for the discontinuous Galerkin method. Zbl 1176.65108
Ryan, Jennifer K.; Cockburn, Bernardo
18
2009
Foreword: Discontinuous Galerkin methods for partial differential equations. Zbl 1203.65005
Cockburn, Bernardo; Shu, Chi-Wang
4
2009
A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. Zbl 1198.65193
Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny
118
2008
An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. Zbl 1187.65110
Nguyen, N. C.; Peraire, J.; Cockburn, B.
109
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
35
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
10
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
89
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
45
2007
Locally conservative fluxes for the continuous Galerkin method. Zbl 1155.65100
Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Wang, Haiying
29
2007
The embedded discontinuous Galerkin method: application to linear shell problems. Zbl 1194.74403
Güzey, S.; Cockburn, B.; Stolarski, H. K.
29
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
Stabilization mechanisms in discontinuous Galerkin finite element methods. Zbl 1125.65102
Brezzi, F.; Cockburn, B.; Marini, L. D.; Süli, E.
57
2006
Hybridized globally divergence-free LDG methods. I: The Stokes problem. Zbl 1087.76061
Carrero, Jesús; Cockburn, Bernardo; Schötzau, Dominik
46
2006
Discontinuous Galerkin methods for incompressible elastic materials. Zbl 1128.74041
Cockburn, Bernardo; Schötzau, Dominik; Wang, Jing
29
2006
Locking-free optimal discontinuous Galerkin methods for Timoshenko beams. Zbl 1127.74041
Celiker, Fatih; Cockburn, Bernardo; Stolarski, Henryk K.
18
2006
Element-by-element post-processing of discontinuous Galerkin methods for Timoshenko beams. Zbl 1099.74062
Celiker, Fatih; Cockburn, Bernardo
10
2006
Design and development of a discontinuous Galerkin method for shells. Zbl 1157.74041
Güzey, S.; Stolarski, H. K.; Cockburn, B.; Tamma, K. K.
7
2006
...and 76 more Documents
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Cited by 4,116 Authors

139 Shu, Chi-Wang
101 Cockburn, Bernardo
54 Dumbser, Michael
41 Qiu, Jianxian
41 Xu, Yan
39 Baccouch, Mahboub
38 Dawson, Clint N.
34 Di Pietro, Daniele Antonio
33 Ye, Xiu
32 Schötzau, Dominik
30 Antonietti, Paola Francesca
30 Cheng, Yingda
30 Li, Fengyan
29 Bassi, Francesco
29 Chung, Tsz Shun Eric
28 Houston, Paul
28 Li, Jichun
26 Ern, Alexandre
26 Qiu, Jingmei
26 van der Vegt, Jaap J. W.
26 Yu, Xijun
25 Liu, Hailiang
25 Zhang, Shangyou
23 Ryan, Jennifer K.
23 Xing, Yulong
22 Huang, Yunqing
22 Mu, Lin
21 Adjerid, Slimane
21 Jameson, Antony
21 Munz, Claus-Dieter
21 Zhang, Zhimin
20 Liu, Tiegang
20 Nguyen, Ngoc Cuong
20 Rivière, Beatrice M.
20 Zhang, Mengping
19 Burman, Erik
19 Dolejší, Vít
19 Fu, Guosheng
19 Giani, Stefano
19 Luo, Hong
19 Xia, Yinhua
19 Zhang, Qiang
18 Balsara, Dinshaw S.
18 Hesthaven, Jan S.
18 Huang, Xuehai
18 Karlsen, Kenneth Hvistendahl
18 Marini, Luisa Donatella
18 Sayas, Francisco-Javier
18 Titi, Edriss Saleh
18 Wang, Junping
17 He, Yinnian
17 Perugia, Ilaria
16 Aizinger, Vadym
16 Bazilevs, Yuri
16 Brezzi, Franco
16 Crivellini, Andrea
16 Gudi, Thirupathi
16 Hughes, Thomas J. R.
16 Kanschat, Guido
16 Kubatko, Ethan J.
16 Rhebergen, Sander
16 Scovazzi, Guglielmo
16 Toro, Eleuterio F.
16 Wheeler, Mary Fanett
16 Wihler, Thomas Pascal
15 Beirão da Veiga, Lourenço
15 Castillo, Paul E.
15 Feistauer, Miloslav
15 Qiu, Weifeng
15 Ruiz-Baier, Ricardo
15 Westerink, Joannes J.
15 Zhang, Yangwen
15 Zhu, Jun
14 Gassner, Gregor J.
14 Gatica, Gabriel N.
14 Guzmán, Johnny
14 Lanteri, Stéphane
14 May, Georg
14 Xu, Jinchao
14 Xu, Kun
13 Celiker, Fatih
13 Chen, Zhangxin
13 Cheng, Jian
13 Persson, Per-Olof
13 Rebay, Stefano
13 Shi, Ke
13 Solano, Manuel E.
13 Wei, LeiLei
13 Xiao, Feng
13 Zhang, Tie
13 Zhang, Xiangxiong
12 Ghidoni, Antonio
12 Guo, Wei
12 Huerta, Antonio
12 Kesserwani, Georges
12 Kronbichler, Martin
12 Li, Maojun
12 Manzini, Gianmarco
12 Pani, Amiya Kumar
12 Remacle, Jean-François
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726 Journal of Computational Physics
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10 Comptes Rendus. Mathématique. Académie des Sciences, Paris
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