An Analysis of the Simplest Mixed Finite Element Method for the Elastic Wave Equation

Abstract

Although it is well-known that there are various mixed finite elements for solving elastic wave equation, in this paper, we will approach the elastic wave equation with 2D, the simplest mixed finite element method. The superiority of the family of elements over the existing elements is its simplicity and high accuracy. It satisfies the discrete inf-sup condition for the stability analysis and has convergence property of the consistency error. In this paper, by using this mixed finite element method, we will get the approximated solution of the elastic wave equation, and also prove that this approximated solution stably converges to real solution through elliptic projection.