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Polyhedral Gauß–Seidel converges
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C. Gräser
Published/Copyright:
October 7, 2014
Abstract
- 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.
Keywords: Allen-Cahn equation; discontinuous Galerkin methods; global convergence; multigrid methods; polyhedral Gauß-Seidel
Published Online: 2014-10-7
Published in Print: 2014-10-1
© 2014 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Discontinuous Galerkin finite element method for plate contact problem with frictional boundary conditions
- A non-conforming composite quadrilateral finite element pair for feedback stabilization of the Stokes equations
- Polyhedral Gauß–Seidel converges
- On the best approximate (P,Q)-orthogonal symmetric and skew-symmetric solution of the matrix equation AXB=C
Keywords for this article
Allen-Cahn equation;
discontinuous Galerkin methods;
global convergence;
multigrid methods;
polyhedral Gauß-Seidel
Articles in the same Issue
- Frontmatter
- Discontinuous Galerkin finite element method for plate contact problem with frictional boundary conditions
- A non-conforming composite quadrilateral finite element pair for feedback stabilization of the Stokes equations
- Polyhedral Gauß–Seidel converges
- On the best approximate (P,Q)-orthogonal symmetric and skew-symmetric solution of the matrix equation AXB=C
