A mass‐lumped mixed FEM for acoustic wave propagation with inhomogeneous coefficients. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Egger, Herbert; Radu, Bogdan
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800325
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: We consider the numerical approximation of acoustic wave propagation in the time domain by a mixed finite element method based on the BDM1 –P0 spaces. In [2], we considered a mass‐lumping strategy for the BDM1 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.