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Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes

✍ Scribed by Mahboub Baccouch; Slimane Adjerid

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
447 KB
Volume
200
Category
Article
ISSN
0045-7825

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✦ Synopsis

Transient convection problems Unstructured meshes a b s t r a c t

We extend the error analysis of Adjerid and Baccouch [1, for the discontinuous Galerkin discretization error to variable-coefficient linear hyperbolic problems as well as nonlinear hyperbolic problems on unstructured meshes. We further extend this analysis to transient hyperbolic problems and prove that the local superconvergence results presented in [1] still hold for both steady and transient variable-coefficient linear and nonlinear problems. This local error analysis allows us to construct asymptotically correct a posteriori error estimates by solving local hyperbolic problems with no boundary conditions on each element of general unstructured meshes. We illustrate the superconvergence and the efficiency of our a posteriori error estimates by showing computational results for several linear and nonlinear numerical examples.

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