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Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations

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Computing and Visualization in Science

Abstract

We consider a Galerkin Finite Element approximation of the Stokes–Darcy problem which models the coupling between surface and groundwater flows. Then we propose an iterative subdomain method for its solution, inspired to the domain decomposition theory. The convergence analysis that we develop is based on the properties of the discrete Steklov–Poincaré operators associated to the given coupled problem. An optimal preconditioner for Krylov methods is proposed and analyzed.

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Authors and Affiliations

  1. Institut de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland

    Marco Discacciati & Alfio Quarteroni

  2. Dipartimento di Matematica, Politecnico di Milano, MOX, P.zza Leonardo da Vinci 32, 20133, Milano, Italy

    Alfio Quarteroni

Authors
  1. Marco Discacciati
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  2. Alfio Quarteroni
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Correspondence to Marco Discacciati.

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Communicated by

M.S. Espedal, A. Quarteroni, A. Sequeira

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Discacciati, M., Quarteroni, A. Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations. Comput Visual Sci 6, 93–103 (2004). https://doi.org/10.1007/s00791-003-0113-0

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  • DOI: https://doi.org/10.1007/s00791-003-0113-0

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