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A high-order HDG method for the Biot’s consolidation model. (English) Zbl 1442.65257

Summary: We propose a novel high-order HDG method for the Biot’s consolidation model in poroelasticity. We present optimal \(h\)-version error analysis for both the semi-discrete and full-discrete (combined with temporal backward differentiation formula) schemes. Numerical tests are provided to demonstrate the performance of the method.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
35Q35 PDEs in connection with fluid mechanics
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