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A mass‐lumped mixed FEM for acoustic wave propagation with inhomogeneous coefficients
Author(s) -
Egger Herbert,
Radu Bogdan
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800325
Subject(s) - finite element method , quadrature (astronomy) , homogeneous , wave propagation , domain (mathematical analysis) , numerical integration , acoustic wave equation , wave equation , time domain , mathematical analysis , mathematics , computer science , acoustic wave , acoustics , physics , statistical physics , quantum mechanics , optics , thermodynamics , computer vision
We consider the numerical approximation of acoustic wave propagation in the time domain by a mixed finite element method based on the BDM 1 –P 0 spaces. In [2], we considered a mass‐lumping strategy for the BDM 1 element that allows for efficient time integration. Moreover, we managed to show that while the accuracy of the method is reduced to first order by the quadrature error, the method does still manage to carry second order global information. This allowed us to devise post‐processing strategies for both variables. Here, we consider the case of inhomogeneous coefficients a and b , and show that the same results hold as for the homogeneous case. In addition, we illustrate the results by a numerical test.