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Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. (English) Zbl 1447.65077

A fixed-stress split method is developed for the flux-based multiple-porosity/multiple-permeability poroelasticity systems describing multiple-network flow and deformation in a poroelastic medium, i.e MPET models. Linear convergence of the method is proved and it is shown that with the proper choice of the stabilization parameter, the rate of convergence is independent of the physical parameters in the model. The performed numerical experiments confirm the convergence rate estimates and demonstrate the efficiency of the presented fixed-stress scheme, the advantage of the fixed-stress split scheme over a preconditioned MinRes solver accelerated by norm-equivalent preconditioning.

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
65F10 Iterative numerical methods for linear systems
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74B20 Nonlinear elasticity
76S05 Flows in porous media; filtration; seepage
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