Stabilized finite elements for time-harmonic elastic waves

Abstract

Standard, low-order, finite element methods for wave phenomena entail considerable computational effort at short wavelengths in order to control numerical dispersion and pollution errors. Stabilized methods such as Galerkin/least-squares combine improvement in performance with simple implementation. The mesh-dependent stability parameter is often defined by dispersion considerations. The application to elastic waves must account for polarization errors as well. The present work extends previous studies by considering two-parameter stabilization for plane elastic waves. A promising definition of the stability parameters eliminates dispersion errors of both longitudinal and transverse waves, but leads to considerable deterioration of the polarization. An alternative definition that eliminates dispersion of longitudinal waves in two directions balances dispersion and polarization errors, and provides the best overall performance.