A sequential discontinuous Galerkin method for the coupling of flow and geomechanics. (English) Zbl 1404.65162
Summary: A decoupled and sequential numerical method is proposed and analyzed for solving the linear poroelasticity equations. Unlike other splitting approaches, this method is not iterative, which results in a speed-up of the computational time. The interior penalty discontinuous Galerkin method is employed for the spatial discretization and is combined with the backward Euler method for the time discretization. We provide a convergence analysis of the scheme along with numerical results that confirm the theoretical results.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-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 |
| 76S05 | Flows in porous media; filtration; seepage |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 86A60 | Geological problems |
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