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| HAL: hal-00707407, version 1 |
| DOI: 10.1142/S0218202512500029 |
| Detailed view |  Export this paper |
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| Mathematical Models and Methods in Applied Sciences 22, 6 (2012) 40 pages |
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| Coupling hererogeneous multiscale fem with Runge-Kutta methods for parabolic homogenization problems: a fully discrete spacetime analysis |
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| Assyr Abdulle 1Gilles Vilmart 2 |
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| (2012) |
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| Numerical methods for parabolic homogenization problems combining finite element methods (FEMs) in space with Runge-Kutta methods in time are proposed. The space discretization is based on the coupling of macro and micro finite element methods following the framework of the Heterogeneous Multiscale Method (HMM). We present a fully discrete analysis in both space and time. Our analysis relies on new (optimal) error bounds in the norms L2(H1), , and for the fully discrete analysis in space. These bounds can then be used to derive fully discrete spacetime error estimates for a variety of Runge-Kutta methods, including implicit methods (e.g. Radau methods) and explicit stabilized method (e.g. Chebyshev methods). Numerical experiments confirm our theoretical convergence rates and illustrate the performance of the methods. |
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| 1: | Ecole Polytechnique Fédérale de Lausanne (EPFL) |
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École Polytechnique Fédérale de Lausanne |
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| 2: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Analyse numérique |
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| Subject | : | Mathematics/Numerical Analysis |
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| Multiple scales – fully discrete – numerical homogenization – finite elements – Runge-Kutta methods – Chebyshev methods – parabolic problems |
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| hal-00707407, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00707407 | |
| oai:hal.archives-ouvertes.fr:hal-00707407 | |
| From: Marie-Annick Guillemer | |
| Submitted on: Tuesday, 12 June 2012 15:54:43 | |
| Updated on: Tuesday, 12 June 2012 15:54:43 | |
