A global space-time Trefftz DG scheme for the time-dependent isotropic elastic wave equations

Long Yuan, Xiaoqiang Yue

Abstract: In this paper we are concerned with Trefftz discretizations of the time-dependent linear elastic wave equation in arbitrary space dimensional domains Ω⊂Rd(d∈N). We propose a Trefftz discontinuous Galerkin method, construct Trefftz basis functions and prove that the corresponding approximate solutions possess optimal-order error estimates with respect to the meshwidth. A space–time domain decomposition preconditioner is introduced for the system generated by the proposed variational formula. Besides, we propose the global Trefftz DG method combined with local DG methods to solve the nonhomogeneous model. The numerical results verify the validity of the theoretical results, and show that the resulting approximate solutions possess high accuracy, and the proposed preconditioner is effective.