Higher order triangular finite elements with mass lumping for the wave equation.

Gary Cohen 1 Patrick Joly 1 Jean E. Roberts Nathalie Tordjman
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In this article, we construct new higher order finite element spaces for the approximation of the two-dimensional (2D) wave equation. These elements lead to explicit methods after time discretization through the use of appropriate quadrature formulas which permit mass lumping. These formulas are constructed explicitly. Error estimates are provided for the corresponding semidiscrete problem. Finally, higher order finite difference time discretizations are proposed and various numerical results are shown.
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Submitted on : Thursday, June 19, 2014 - 4:03:25 PM
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Gary Cohen, Patrick Joly, Jean E. Roberts, Nathalie Tordjman. Higher order triangular finite elements with mass lumping for the wave equation.. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2001, 38 (6), pp.2047-2078. ⟨10.1137/S0036142997329554⟩. ⟨hal-01010373⟩

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