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Robust block preconditioners for Biot’s model. (English) Zbl 1442.65342

Bjørstad, Petter E. (ed.) et al., Domain decomposition methods in science and engineering XXIV. Proceedings of the 24th international conference, Svalbard, Norway, February 6–10, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 125, 3-16 (2018).
Summary: In this paper, we design robust and efficient block preconditioners for the two-field formulation of Biot’s consolidation model, where stabilized finite-element discretizations are used. The proposed block preconditioners are based on the well-posedness of the discrete linear systems. Block diagonal (norm-equivalent) and block triangular preconditioners are developed, and we prove that these methods are robust with respect to both physical and discretization parameters. Numerical results are presented to support the theoretical results.
For the entire collection see [Zbl 1430.65002].

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
74B10 Linear elasticity with initial stresses
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
65F10 Iterative numerical methods for linear systems
65F08 Preconditioners for iterative methods
76M10 Finite element methods applied to problems in fluid mechanics
74S05 Finite element methods applied to problems in solid mechanics
35Q35 PDEs in connection with fluid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
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