A Weak Galerkin Mixed Finite Element Method for AcousticWave Equation

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 k0 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 fullydiscrete schemes,and obtain the suboptimal order error estimates for the velocity and pressure variables.Numerical experiment confirms our theoretical analysis.