Author(s)

P. Tarvainen

Abstract

Overlapping block relaxation methods are applied to the iterative solution of algebraic obstacle problems with M-matrices. Such problems arise, eg., from finite element approximation of obstacle problems with diffusion or convection-diffusion operators. We propose and analyze various algorithms with the emphasis on their monotonicity properties: the methods are mono- tonically convergent in the subset of supersolutions, and their asymptotic convergence rates can be evaluated in this particular subset. We also discuss the multilevel approach within the block relaxation methods; this approach makes possible to choose individual subproblem solvers for the methods. Numerical experiments are included to illustrate the theoretical results. 1

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