Uniform Convergence of Adaptive Multigrid Methods for Elliptic Problems and Maxwell’s Equations
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Author / Producer
Date
2012-08
Publication Type
Journal Article
ETH Bibliography
yes
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Abstract
We consider the convergence theory of adaptive multigrid methods for second-order elliptic problems and Maxwell's equations. The multigrid algorithm only performs pointwise Gauss-Seidel relaxations on new degrees of freedom and their "immediate" neighbors. In the context of lowest order conforming finite element approximations, we present a unified proof for the convergence of adaptive multigrid V-cycle algorithms. The theory applies to any hierarchical tetrahedral meshes with uniformly bounded shape-regularity measures. The convergence rates for both problems are uniform with respect to the number of mesh levels and the number of degrees of freedom. We demonstrate our convergence theory by two numerical experiments.
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published
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Book title
Journal / series
Volume
5 (3)
Pages / Article No.
297 - 332
Publisher
Global Science Press
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Edition / version
Methods
Software
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Date collected
Date created
Subject
MMaxwell's equations; Lagrangian finite elements; Edge elements; Adaptive multigrid method; Successive subspace correction
Organisational unit
03632 - Hiptmair, Ralf / Hiptmair, Ralf
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher