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Domain Decomposition Methods in Science and Engineering XXIII pp 3–16Cite as

Global Convergence Rates of Some Multilevel Methods for Variational and Quasi-Variational Inequalities

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 116))

Abstract

We introduce some multilevel and multigrid methods and derive their global convergence rate for variational inequalities and for variational inequalities containing a term introduced by a nonlinear operator. Also, we estimate the convergence rate of the one- and two-level methods for variational inequalities of the second kind and for quasi-variational inequalities. The methods are introduced as subspace correction algorithms in a reflexive Banach space, where general convergence results are derived. These algorithms become multilevel and multigrid methods by introducing the finite element spaces. In this case, the error estimates are written in function of the number of subdomains and the overlapping parameter for the one- and two-level methods, and in function of the number of levels for the multigrid methods. The obtained convergence rates for the multigrid methods are compared with those existing in the literature for the complementarity problems.

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Authors and Affiliations

  1. Institute of Mathematics of the Romanian Academy, 1-764, RO-014700, Bucharest, Romania

    Lori Badea

Authors
  1. Lori Badea
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Correspondence to Lori Badea .

Editor information

Editors and Affiliations

  1. Dept. of Mathematical Sciences, KAIST, Daejeon, Korea (Republic of)

    Chang-Ock Lee

  2. Dept. of Computer Science, University of Colorado, Boulder, Colorado, USA

    Xiao-Chuan Cai

  3. Applied Math & Computational Science, KAUST, Thuwal, Saudi Arabia

    David E. Keyes

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

    Hyea Hyun Kim

  5. Mathematisches Institut, Universität zu Köln, Köln, Germany

    Axel Klawonn

  6. Dept. of Computational Science & Engineering, Yonsei University, Seoul, Korea (Republic of)

    Eun-Jae Park

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

    Olof B. Widlund

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Badea, L. (2017). Global Convergence Rates of Some Multilevel Methods for Variational and Quasi-Variational Inequalities. In: Lee, CO., et al. Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-52389-7_1

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