Dispersion analysis of discontinuous Galerkin method on triangular mesh for elastic wave equation

• Numerical dispersion of P1 discontinuous Galerkin is too high for seismic modelling.
• Numerical dispersion of P2 DG is close to that of the 4-th order finite differences.
• P3 and higher order DG are accurate but computationally intense.
• P2 DG is the optimal formulation for seismic modeling.

This paper presents a mid-frequency dispersion analysis of the triangle-based discontinuous Galerkin method for numerical simulation of seismic wave propagation. The results for different orders of basis polynomials are presented and compared with the finite difference approximations. It is shown that the dispersion error of the P1 DG is higher than that of the second order standard staggered grid scheme if the dispersion error is considered with respect to the degrees of freedom per wavelength, and the error of P2 is close to that of the fourth order scheme, whereas a further increase in the polynomial order makes it possible to simulate seismic waves using as coarse discretization as 2 grid cells per wavelength however computational intensity of the algorithm becomes unreasonably high.