Influence of Gauss and Gauss-Lobatto quadrature rules on the accuracy of a quadrilateral finite element method in the time domain.

Marc Durufle 1 Pascal Grob 1 Patrick Joly 1
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 paper, we examine the infl uence of numerical integration on finite element methods using quadrilateral or hexahedral meshes in the time domain. We pay special attention to the use of Gauss-Lobatto points to perform mass lumping for any element order. We provide some theoretical results through several error estimates that are completed by various numerical experiments.
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Marc Durufle, Pascal Grob, Patrick Joly. Influence of Gauss and Gauss-Lobatto quadrature rules on the accuracy of a quadrilateral finite element method in the time domain.. Numerical Methods for Partial Differential Equations, Wiley, 2009, 25 (3), pp.526-551. ⟨10.1002/num.20353⟩. ⟨hal-00403791⟩

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