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International Conference on Domain Decomposition Methods

DD 2017: Domain Decomposition Methods in Science and Engineering XXIV pp 119–127Cite as

Restricted Additive Schwarz Method for Some Inequalities Perturbed by a Lipschitz Operator

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 125))

Abstract

We introduce and analyze a restricted additive Schwarz method for some inequalities perturbed by a Lipschitz operator. An existence and uniqueness result concerning the solution of the inequalities we consider is given. Also, we introduce the method as a subspace correction algorithm, prove the convergence and estimate the error in a general framework of a finite dimensional Hilbert space. By introducing the finite element spaces, we get that our algorithm is really a restricted additive Schwarz method and conclude that the convergence condition and convergence rate are independent of the mesh parameters and of both the number of subdomains and the parameters of the domain decomposition, but the convergence condition is a little more restrictive than the existence and uniqueness condition of the solution.

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References

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Authors and Affiliations

  1. Institute of Mathematics of the Romanian Academy, Francophone Center for Mathematics in Bucharest, Bucharest, Romania

    Lori Badea

Authors
  1. Lori Badea
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Correspondence to Lori Badea .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petter E. Bjørstad

  2. Department of Mathematics, Louisana State University, Baton Rouge, LA, USA

    Susanne C. Brenner

  3. Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

    Lawrence Halpern

  4. Department of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Ralf Kornhuber

  6. Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

  7. Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

    Olof B. Widlund

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Badea, L. (2018). Restricted Additive Schwarz Method for Some Inequalities Perturbed by a Lipschitz Operator. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_9

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