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Discontinuous Galerkin methods on hp-anisotropic meshes I: A priori error analysis
| Content Provider | CiteSeerX |
|---|---|
| Author | Georgoulis, Emmanuil H. Hall, Edward Houston, Paul |
| Abstract | We consider the a posteriori error analysis and hp-adaptation strate-gies for hp-version interior penalty discontinuous Galerkin methods for second–order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes with anisotropically enriched elemental polynomial degrees. In particular, we exploit duality based hp-error estimates for linear target functionals of the solution and design and implement the corresponding adaptive algorithms to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement and isotropic and anisotropic polyno-mial degree enrichment. The superiority of the proposed algorithm in comparison with standard hp–isotropic mesh refinement algorithms and an h–anisotropic/p–isotropic adaptive procedure is illustrated by a series of numerical experiments. 1 |
| File Format | |
| Journal | International Journal of Computing Science and Mathematics |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Discontinuous Galerkin Method Priori Error Analysis Hp-anisotropic Mesh Anisotropic Isotropic Adaptive Procedure Posteriori Error Analysis Numerical Experiment Elemental Polynomial Degree Efficient Control Corresponding Adaptive Algorithm Computational Mesh Local Isotropic Nonnegative Characteristic Form Hp-error Estimate Linear Target Functionals Second Order Partial Differential Equation Hp-adaptation Strate-gies Anisotropic Polyno-mial Degree Enrichment Anisotropic Mesh Refinement |
| Content Type | Text |
| Resource Type | Article |
