Repository: Freie Universit├Ąt Berlin, Math Department

Monotone multigrid methods for elliptic variational inequalities I

Kornhuber, R. (1994) Monotone multigrid methods for elliptic variational inequalities I. Numerische Mathematik, 69 (2). pp. 167-184. ISSN 0029-599X

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Official URL: http://dx.doi.org/10.1007/BF03325426

Abstract

We derive fast solvers for discrete elliptic variational inequalities of the first kind (obstacle problems) as resulting from the approximation of related continuous problems by piecewise linear finite elements. Using basic ideas of successive subspace correction, we modify well-known relaxation methods by extending the set of search directions. Extended underrelaxations are called monotone multigrid methods, if they are quasioptimal in a certain sense. By construction, all monotone multigrid methods are globally convergent. We take a closer look at two natural variants, the standard monotone multigrid method and a truncated version. For the considered model problems, the asymptotic convergence rates resulting from the standard approach suffer from insufficient coarse-grid transport, while the truncated monotone multigrid method provides the same efficiency as in the unconstrained case.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Numerical Analysis
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:1914
Deposited By: Ekaterina Engel
Deposited On:21 Jun 2016 20:29
Last Modified:03 Mar 2017 14:42

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