Year: 2022
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 4 : pp. 936–959
Abstract
This paper is concerned with the weak Galerkin mixed finite element method (WG-MFEM) for the second-order hyperbolic acoustic wave equation in velocity-pressure formulation. In this formulation, the original second-order differential equation in time and space is reduced to first-order differential equations by introducing the velocity and pressure variables. We employ the usual discontinuous piecewise-polynomials of degree $k\geq 0$ for the pressure and $k+1$ for the velocity. Furthermore, the normal component of the pressure on the interface of elements is enhanced by polynomials of degree $k+1$. The time derivative is approximated by the backward Euler difference. We show the stability of the semi-discrete and fully-discrete schemes, and obtain the suboptimal order error estimates for the velocity and pressure variables. Numerical experiment confirms our theoretical analysis.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0346
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 4 : pp. 936–959
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Acoustic wave equation velocity-pressure formulation WG-MFEM.
-
Mixed Virtual Element approximation of linear acoustic wave equation
Dassi, Franco
Fumagalli, Alessio
Mazzieri, Ilario
Vacca, Giuseppe
IMA Journal of Numerical Analysis, Vol. 44 (2024), Iss. 5 P.2864
https://doi.org/10.1093/imanum/drad078 [Citations: 0]