Discontinuous Galerkin method for the fully dynamic Biot’s model. (English) Zbl 1464.65188
Summary: In this paper, a fully discrete scheme of the fully dynamic Biot’s model problem is proposed, which is constructed by using interior penalty discontinuous Galerkin method for the spatial approximation and a tailor difference scheme to approximate the first and second order temporal derivative terms. First of all, we prove the existence and uniqueness of solutions of proposed fully discrete scheme in proper norms. Then, based on the error equations a priori error estimates shall be derived for both primal variables displacement and pore pressure. Finally, a series of numerical examples are given to examine the convergence results by using the proposed numerical scheme to solve the fully dynamic Biot’s model problem.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving 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 |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
Keywords:
fully dynamic Biot’s model; discontinuous Galerkin method; fully discrete scheme; a priori error estimatesReferences:
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