The Discontinuous Galerkin Method for Two-dimensional Hyperbolic Problems Part II: A Posteriori Error Estimation

Authors:
Slimane Adjerid;Mahboub Baccouch
Affiliations:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, USA 24061;Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, USA 24061
Venue:
Journal of Scientific Computing
Year:
2009

Citing 11
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Abstract

In this manuscript we construct simple, efficient and asymptotically correct a posteriori error estimates for discontinuous finite element solutions of scalar first-order hyperbolic partial differential problems on triangular meshes. We explicitly write the basis functions for the error spaces corresponding to several finite element spaces. The leading term of the discretization error on each triangle is estimated by solving a local problem. We also show global superconvergence for discontinuous solutions on triangular meshes. The a posteriori error estimates are tested on several linear and nonlinear problems to show their efficiency and accuracy under mesh refinement for smooth and discontinuous solutions.