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.
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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.
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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: 1]