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A nodal discontinuous Galerkin finite element method for the poroelastic wave equation. (English) Zbl 1422.65267

Summary: We use the nodal discontinuous Galerkin method with a Lax-Friedrich flux to model the wave propagation in transversely isotropic and poroelastic media. The effect of dissipation due to global fluid flow causes a stiff relaxation term, which is incorporated in the numerical scheme through an operator splitting approach. The well-posedness of the poroelastic system is proved by adopting an approach based on characteristic variables. An error analysis for a plane wave propagating in poroelastic media shows a convergence rate of \(O(h^{n+1})\). Computational experiments are shown for various combinations of homogeneous and heterogeneous poroelastic media.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q74 PDEs in connection with mechanics of deformable solids
74J05 Linear waves in solid mechanics
74J10 Bulk waves in solid mechanics
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