Space-time discontinuous Galerkin method for advection-diffusion problems on time-dependent domains
| Autor: | R.M.J. van Damme, J.J.W. van der Vegt, J.J. Sudirham |
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| Rok vydání: | 2006 |
| Předmět: |
Numerical Analysis
MSC-76M10 Discretization IR-63814 Function space EWI-8539 Applied Mathematics Numerical analysis Mathematical analysis MSC-65M60 Basis function Finite element method Computational Mathematics MSC-35K20 Discontinuous Galerkin method Discontinuous Galerkin parabolic problem Convection–diffusion equation METIS-237782 time-dependent domain Discretization of continuous features Mathematics |
| Zdroj: | Applied numerical mathematics, 56(suppl 2/12):10.1016/j.apnum.2005.11.003, 1491-1518. Elsevier |
| ISSN: | 0168-9274 |
| DOI: | 10.1016/j.apnum.2005.11.003, |
| Popis: | This article presents a space–time discontinuous Galerkin (DG) finite element discretization of the advection–diffusion equation on time-dependent domains. In the space–time DG discretization no distinction is made between the space and time variables and discontinuous basis functions are used both in space and time. This approach results in an efficient numerical technique for physical applications which require moving and deforming elements, is suitable for hp-adaptation and results in a fully conservative discretization. A complete derivation of the space–time DG method for the advection–diffusion equation is given, together with the relation of the space–time discretization with the arbitrary Lagrangian Eulerian (ALE) approach. Detailed proofs of stability and error estimates are also provided. The space–time DG method is demonstrated with numerical experiments that agree well with the error analysis. |
| Databáze: | OpenAIRE |
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