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The Discontinuous Galerkin Method for Two-dimensional Hyperbolic Problems

Summary: The Discontinuous Galerkin Method for
Two-dimensional Hyperbolic Problems
Part II: A posteriori Error Estimation
Slimane Adjerid and Mahboub Baccouch
Department of Mathematics
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061
August 24, 2007
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.
Keywords: Discontinuous Galerkin method; hyperbolic problems; superconver-
gence; a posteriori error estimation.


Source: Adjerid, Slimane - Department of Mathematics, Virginia Tech


Collections: Mathematics