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A new discontinuous Galerkin method for elastic waves with physically motivated numerical fluxes. (English) Zbl 1506.65151

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.
Reviewer: Yan Xu (Hefei)

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35F55 Initial value problems for systems of nonlinear first-order PDEs
35F46 Initial-boundary value problems for systems of linear first-order PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
74J05 Linear waves in solid mechanics
74M10 Friction in solid mechanics
74R10 Brittle fracture
35Q74 PDEs in connection with mechanics of deformable solids

Software:

ExaHyPE; Peano; p4est
PDFBibTeX XMLCite
Full Text: DOI

References:

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