Repository: Freie Universität Berlin, Math Department

Polyhedral Gauß-Seidel converges

Gräser, C. and Sander, O. (2014) Polyhedral Gauß-Seidel converges. Journal of Numerical Mathematics, 22 (3). pp. 221-254. ISSN 1570-2820


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We prove global convergence of an inexact extended polyhedral Gauß-Seidel method for the minimization of strictly convex functionals that are continuously differentiable on each polyhedron of a polyhedral decomposition of their domains of definition. While pure Gauß-Seidel methods are known to be very slow for problems governed by partial differential equations, the presented convergence result also covers multilevel methods that extend the Gauß-Seidel step by coarse level corrections. Our result generalizes the proof of [10] for differentiable functionals on the Gibbs simplex. Example applications are given that require the generality of our approach.

Item Type:Article
Uncontrolled Keywords:Allen-Cahn equation, discontinuous Galerkin methods, global convergence, multigrid methods, polyhedral Gauß-Seidel
Subjects:Mathematical and Computer Sciences > Mathematics > Numerical Analysis
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:1789
Deposited By: Ekaterina Engel
Deposited On:17 Feb 2016 09:49
Last Modified:03 Mar 2017 14:41

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