The discontinuous Galerkin method for two-dimensional hyperbolic problems part II: A posteriori error estimation

Slimane Adjerid; Mahboub Baccouch

doi:10.1007/s10915-008-9222-8

The discontinuous Galerkin method for two-dimensional hyperbolic problems part II: A posteriori error estimation

Slimane Adjerid, Mahboub Baccouch

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

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.

Original language	English (US)
Pages (from-to)	15-49
Number of pages	35
Journal	Journal of Scientific Computing
Volume	38
Issue number	1
DOIs	https://doi.org/10.1007/s10915-008-9222-8
State	Published - Jan 2009
Externally published	Yes

Keywords

A posteriori error estimation
Discontinuous Galerkin method
Hyperbolic problems
Superconvergence

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
Engineering(all)
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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10.1007/s10915-008-9222-8

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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.",

keywords = "A posteriori error estimation, Discontinuous Galerkin method, Hyperbolic problems, Superconvergence",

author = "Slimane Adjerid and Mahboub Baccouch",

note = "Funding Information: Acknowledgement This research was partially supported by the National Science Foundation (Grant Number DMS 0511806).",

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AU - Baccouch, Mahboub

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AB - 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.

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KW - Discontinuous Galerkin method

KW - Hyperbolic problems

KW - Superconvergence

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The discontinuous Galerkin method for two-dimensional hyperbolic problems part II: A posteriori error estimation

Abstract

Keywords

ASJC Scopus subject areas

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