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Multigrid Methods for Discrete Elliptic Problems on Triangular Surfaces

Please always quote using this URN:urn:nbn:de:0296-matheon-4237
  • We construct and analyze multigrid methods for discretized self-adjoint elliptic problems on triangular surfaces in $\RR^3$. The methods involve the same weights for restriction and prolongation as in the case of planar triangulations and therefore are easy to implement. We prove logarithmic bounds of the convergence rates with constants solely depending on the ellipticity, the smoothers and on the regularity of the triangles forming the triangular surface. Our theoretical results are illustrated by numerical computations.

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Metadaten
Author:Ralf Kornhuber, Harry Yserentant
URN:urn:nbn:de:0296-matheon-4237
Referee:Konrad Polthier
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2007/10/17
Release Date:2007/10/17
Institute:Freie Universität Berlin
Technische Universität Berlin
MSC-Classification:53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx) / 53Cxx Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx] / 53C44 Geometric evolution equations (mean curvatureGeometric evolution equations (mean curvature flow, Ricci flow, etc.)
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N55 Multigrid methods; domain decomposition
Preprint Number:411
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