The discontinuous Galerkin method (DGM) has been applied to investigate seismic wave propagation recently. However, few studies have examined the dispersion property of DGM with different basis functions. Therefore, three common basis functions, Legendre polynomial, Lagrange polynomial with equidistant nodes, and Lagrange polynomial with Gauss-Lobatto-Legendre (GLL) nodes, are used for numerical approximation. The numerical dispersion and anisotropy numerical behavior of acoustic and elastic waves are compared, and the numerical errors of different order methods are analyzed. The result shows that the dispersion errors for all basis functions reduce generally with increasing interpolation orders, but with large differences in different directions. Specifically, the Legendre basis function and Lagrange basis function with GLL nodes have attractive advantages over the Lagrange polynomial with equidistant nodes for numerical computation. We verified the dispersion properties by theoretical and numerical analyses.
An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media