Numerical solution of the acoustic wave equation using Raviart–Thomas elements

摘要

In this paper we discuss the numerical approximation of the displacement form of the acoustic wave equation using mixed finite elements. The mixed formulation allows for approximation of both displacement and pressure at each time step, without the need for post-processing. Lowest-order and next-to-lowest-order Raviart–Thomas elements are used for the spatial discretization, and centered finite differences are used to advance in time. Use of these Raviart–Thomas elements results in a diagonal mass matrix for resolution of pressure, and a mass matrix for the displacement variable that is sparse with a simple structure. Convergence results for a model problem are provided, as are numerical results for a two-dimensional problem with a point source.