Mixed Finite Elements, Strong Symmetry and Mass Lumping for Elastic WavesReport as inadecuate




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1 ONDES - Modeling, analysis and simulation of wave propagation phenomena Inria Paris-Rocquencourt, Univ. Paris-Saclay, ENSTA ParisTech - École Nationale Supérieure de Techniques Avancées, CNRS - Centre National de la Recherche Scientifique : UMR2706

Abstract : We present here the continuation of our work on mixed finite elements for wave propagation problems. In a previous report, we constructed and analysed a new family of quadrangular 2D or cubic 3D mixed finite elements, for the approximation of the scalar anisotropic wave equation. This work is extended here to the elastic wave equation, including in the case of an anisotropic medium. These new elements present the specificity to enforce the symmetry of the stress tensor in a str ong way and lead to explicit schemes via mass lumping, after time discretization. The convergence analysis of these mixed finite elements is not straightforward: neither the standard abstract theory nor the theory we developed for the scalar case can be applied. That is why we introduce a new abstract theory which allows to get error estimates.

Keywords : ANISOTROPIC ELASTIC WAVES MASS LUMPING MIXED FINITE ELEMENTS





Author: Eliane Bécache - Patrick Joly - Chrysoula Tsogka -

Source: https://hal.archives-ouvertes.fr/



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