A new discontinuous Galerkin method for elastic waves with physically motivated numerical fluxes (Q2051057)

The paper presents a stable and arbitrary order accurate discontinuous Galerkin (DG) method for elastic waves with a physically motivated numerical flux. The numerical flux is compatible with well-posed, internal and external, boundary conditions, including linear and nonlinear frictional constitutive equations for modeling spontaneously propagating shear ruptures in elastic solids and dynamic earthquake rupture processes. The choice of penalty parameters yields an upwind scheme and a discrete energy estimate analogous to the continuous energy estimate. A priori error estimate for the DG method is provided. Numerical experiments in one and two space dimensions verify high-order accuracy and asymptotic numerical stability. The potential of the method for modeling complex nonlinear frictional problems in elastic solids with 2D dynamically adaptive meshes and non-planar topography with 2D curvilinear elements are demonstrated.