A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems

Adjerid, 2002, A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems, Comput. Methods Appl. Mech. Engrg., 191, 1097, 10.1016/S0045-7825(01)00318-8 Bassi, 1997, A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier–Stokes equations, J. Computat. Phys., 131, 267, 10.1006/jcph.1996.5572 Baumann, 1999, A discontinuous hp finite element method for convection-diffusion problems, Comput. Methods Appl. Mech. Engrg., 175, 311, 10.1016/S0045-7825(98)00359-4 Bey, 1996, hp-version discontinuous Galerkin method for hyperbolic conservation laws, Comput. Methods Appl. Mech. Engrg., 133, 259, 10.1016/0045-7825(95)00944-2 Bey, 1995, hp-version discontinuous Galerkin method for hyperbolic conservation laws: a parallel strategy, Int. J. Numer. Methods Engrg., 38, 3889, 10.1002/nme.1620382209 Bey, 1996, A parallel hp-adaptive discontinuous Galerkin method for hyperbolic conservation laws, Appl. Numer. Math., 20, 321, 10.1016/0168-9274(95)00101-8 Biswas, 1994, Parallel adaptive finite element methods for conservation laws, Appl. Numer. Math., 14, 255, 10.1016/0168-9274(94)90029-9 Cockburn, 1999, A simple introduction to error estimation for nonlinear hyperbolic conservation laws, vol. 26, 1 Cockburn, 1996, Error estimates for finite element methods for nonlinear conservation laws, SIAM J. Numer. Anal., 33, 522, 10.1137/0733028 2000, vol. 11 Cockburn, 1989, TVB Runge–Kutta local projection discontinuous Galerkin methods of scalar conservation laws III: One dimensional systems, J. Computat. Phys., 84, 90, 10.1016/0021-9991(89)90183-6 Cockburn, 1989, TVB Runge–Kutta local projection discontinuous Galerkin methods for scalar conservation laws II: General framework, Math. Computat., 52, 411 Devine, 1996, Parallel adaptive hp-refinement techniques for conservation laws, Comput. Methods Appl. Mech. Engrg., 20, 367 Ericksson, 1991, Adaptive finite element methods for parabolic problems I: A linear model problem, SIAM J. Numer. Anal., 28, 12 Ericksson, 1995, Adaptive finite element methods for parabolic problems II: Optimal error estimates in l∞l2 and l∞l∞, SIAM J. Numer. Anal., 32, 706, 10.1137/0732033 Flaherty, 1997, Adaptive local refinement with octree load-balancing for the parallel solution of three-dimensional conservation laws, J. Parallel Distrib. Comput., 47, 139, 10.1006/jpdc.1997.1412 Johnson, 1987 L. Krivodonova, J.E. Flaherty, Error estimation for discontinuous Galerkin solutions of multidimensional hyperbolic problems, submitted for publication. Proceedings of the Com2 MaC Conference on Computational Mathematics, to appear Larson, 2000, A posteriori error estimation for adaptive discontinuous Galerkin approximation of hyperbolic systems W.H. Reed, T.R. Hill, Triangular mesh methods for the neutron transport equation, Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory, Los Alamos, 1973 B. Rivière, M.F. Wheeler, A posteriori error estimation and mesh adaptation strategy for discontinuous Galerkin methods applied to diffusion problems, TICAM Report 00-10, 2000 Süli, 1999, A posteriori error analysis and adaptivity for finite element approximations of hyperbolic problems, vol. 5 Wheeler, 1978, An elliptic collocation-finite element method with interior penalties, SIAM J. Numer. Anal., 15, 152, 10.1137/0715010