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Baccouch, Mahboub; Adjerid, Slimane

Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes. (English) Zbl 1225.76190

Comput. Methods Appl. Mech. Eng. 200, No. 1-4, 162-177 (2011).
Summary: We extend the error analysis 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 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.

Cited in 1 Review
Cited in 26 Documents

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76R99 Diffusion and convection
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

discontinuous Galerkin method; hyperbolic problems; superconvergence; A posteriori error estimation; transient convection problems; unstructured meshes
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References:

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