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Domain decomposition and splitting methods for Mortar mixed finite element approximations to parabolic equations

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Summary

We introduce in this article a new domain decomposition algorithm for parabolic problems that combines Mortar Mixed Finite Element methods for the space discretization with operator splitting schemes for the time discretization. The main advantage of this method is to be fully parallel. The algorithm is proven to be unconditionally stable and a convergence result in\(\mathcal{O}\) (Δt/h 1/2) is presented.

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Authors and Affiliations

  1. Division Informatique Scientifique et Mathématiques Appliquées, Institut Français du Pétrole, 92852, Rueil Malmaison Cedex, France

    Stéphanie Gaiffe & Roland Masson

  2. Department of Mathematics, University of Houston, 4800 Calhoun Rd, 77204-3476, Houston, TX, USA

    Roland Glowinski

Authors
  1. Stéphanie Gaiffe
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  2. Roland Glowinski
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  3. Roland Masson
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Correspondence to Roland Glowinski.

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Gaiffe, S., Glowinski, R. & Masson, R. Domain decomposition and splitting methods for Mortar mixed finite element approximations to parabolic equations. Numer. Math. 93, 53–75 (2002). https://doi.org/10.1007/BF02679437

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  • DOI: https://doi.org/10.1007/BF02679437

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