The Ultra-Weak Variational Formulation for Elastic Wave Problems

Abstract

The ultra-weak variational formulation has been used effectively to solve time-harmonic acoustic and electromagnetic wave propagation in inhomogeneous media. We develop the ultra-weak variational formulation for elastic wave propagation in two space dimensions. In order to improve the accuracy and stability of the method, we find it necessary to approximate the S- and P-wave components of the solution in a balanced way. Some preliminary analysis is provided and numerical evidence is presented for the efficiency of the scheme in comparison to piecewise linear finite elements.