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A finite element method with strong mass conservation for Biot’s linear consolidation model. (English) Zbl 1407.65192

Summary: An \(\mathrm{H}(\mathrm{div})\) conforming finite element method for solving the linear Biot equations is analyzed. Formulations for the standard mixed method are combined with formulation of interior penalty discontinuous Galerkin method to obtain a consistent scheme. Optimal convergence rates are obtained.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin 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
35Q74 PDEs in connection with mechanics of deformable solids
35Q35 PDEs in connection with fluid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics

Software:

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References:

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