An Error Analysis of Conservative Space-Time Mesh Refinement Methods for the 1D Wave Equation

Patrick Joly 1 Jerónimo Rodríguez 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We study two space-time mesh refinement methods as the one introduced in [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 197-221].The stability of such methods is guaranteed by construction through the conservation of a discrete energy. In this paper, we show the L 2 convergence of these schemes and provide optimal error estimates. The proof is based on energy techniques and bootstrap arguments. Our results are validated with numerical simulations and compared with results from plane wave analysis [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 223-251].
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Article dans une revue
SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2005, 43, pp.825-859. <10.1137/040603437>
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Soumis le : vendredi 25 avril 2014 - 10:32:31
Dernière modification le : jeudi 9 février 2017 - 15:47:30

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Patrick Joly, Jerónimo Rodríguez. An Error Analysis of Conservative Space-Time Mesh Refinement Methods for the 1D Wave Equation. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2005, 43, pp.825-859. <10.1137/040603437>. <hal-00983322>

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