Gräser, C. and Sander, O. (2014) Polyhedral GaußSeidel converges. Journal of Numerical Mathematics, 22 (3). pp. 221254. ISSN 15702820

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Official URL: http://dx.doi.org/10.1515/jnma20140010
Abstract
We prove global convergence of an inexact extended polyhedral GaußSeidel 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 GaußSeidel 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 GaußSeidel 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:  AllenCahn equation, discontinuous Galerkin methods, global convergence, multigrid methods, polyhedral GaußSeidel 
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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