Improved finite element methods for elastic waves

Abstract

In this work we develop finite element methods for exterior problems of time-harmonic elastic waves. We employ DtN exterior boundary conditions on an artificial boundary to obtain a well-posed equivalent problem in a bounded region that is suitable for domain-based computation. Galerkin, Galerkin/least-squares and Galerkin/gradient least-squares finite element methods are presented. In acoustic wave problems the Galerkin/least-squares method counters the numerical difficulties that result from employing the Galerkin method, but proves to be insufficient for elastic waves. A specialization of the Galerkin/gradient least-squares method to problems of elastic waves yields good results. Numerical tests validate these conclusions.