WIAS Preprint No. 1812, (2013)

On iterative subdomain methods for the Stokes--Darcy problem



Authors

  • Caiazzo, Alfonso
    ORCID: 0000-0002-7125-8645
  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Wilbrandt, Ulrich

2010 Mathematics Subject Classification

  • 65N30 65N55

Keywords

  • Stokes--Darcy problem, iterative subdomain methods, Robin boundary conditions, finite element methods, continuous and discontinuous, updating strategy, applications from geosciences

Abstract

Iterative subdomain methods for the Stokes--Darcy problem that use Robin boundary conditions on the interface are reviewed. Their common underlying structure and their main differences are identified. In particular, it is clarified that there are different updating strategies for the interface conditions. For small values of fluid viscosity and hydraulic permeability, which are relevant in applications from geosciences, it is shown in numerical studies that only one of these updating strategies leads to an efficient numerical method, if this strategy is used in combination with appropriate parameters in the Robin boundary conditions. In particular, it is observed that the values of appropriate parameters are larger than those proposed so far. Not only the size but also the ratio of appropriate Robin parameters depends on the coefficients of the problem.

Appeared in

  • Comput. Geosci., 18 (2014) pp. 711--728.

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