A Decoupled Preconditioning Technique for a Mixed Stokes---Darcy Model

Authors:
Antonio Márquez;Salim Meddahi;Francisco-Javier Sayas
Affiliations:
Departamento de Construcción e Ingeniería de Fabricación, Universidad de Oviedo, Oviedo, Spain;Departamento de Matemáticas, Facultad de Ciencias, Universidad de Oviedo, Oviedo, Spain;Department of Mathematical Sciences, University of Delaware, Newark, USA 19716
Venue:
Journal of Scientific Computing
Year:
2013

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Abstract

We propose an efficient iterative method to solve the mixed Stokes---Darcy model for coupling fluid and porous media flow. The weak formulation of this problem leads to a coupled, indefinite, ill-conditioned and symmetric linear system of equations. We apply a decoupled preconditioning technique requiring only good solvers for the local mixed-Darcy and Stokes subproblems. We prove that the method is asymptotically optimal and confirm, with numerical experiments, that the performance of the preconditioners does not deteriorate on arbitrarily fine meshes.