A Trefftz-discontinuous Galerkin method for time-harmonic elastic wave problems.

In this paper, we develop a plane wave discontinuous Galerkin method combined with local spectral element method for the elastic wave propagation in two and three space dimensions. We derive the error estimates of the approximation solutions in the mesh-dependent norm and the mesh-independent norm. Some dependence of the error bounds on the orders q of local spectral elements and the number p of plane wave propagation directions is given. Numerical results assess the validity of the theoretical results and indicate that the resulting approximate solutions generated by the PWDG–LSFE possess high accuracy. [ABSTRACT FROM AUTHOR]