(untitled) (Advances in Applied Mathematics and Mechanics, 2022)
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≥ 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.