Calculating Numeric Dispersive Properties Of Fem's For The 2d And 3d Elastic Wave Equation

Abstract

We investigate the numerical dispersive properties of nonconforming nite
element methods to solve the two and three dimensional elastodynamic equations. The
study is performed by deriving and analysing the dispersion relations and by evaluating
the derived quantities, such as the dimension-less phase and group velocities. Also the
phase dierence between exact and numerical solutions is investigated. The method studied,
which yields a linear spatial approximation, demonstrates to be less dispersive than
conforming bilinear nite element methods yielding the same spatial degree of approximation
in the two cases shown herein.