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Erschienen in:
2017 | OriginalPaper | Buchkapitel
Global Convergence Rates of Some Multilevel Methods for Variational and Quasi-Variational Inequalities
verfasst von : Lori Badea
Erschienen in: Domain Decomposition Methods in Science and Engineering XXIII
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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.