Local multilevel methods for adaptive nonconforming finite element methods

  • In this paper, we propose a local multilevel product algorithm and its additive version for linear systems arising from adaptive nonconforming finite element approximations of second order elliptic boundary value problems. The abstract Schwarz theory is applied to analyze the multilevel methods with Jacobi or Gauss-Seidel smoothers performed on local nodes on coarse meshes and global nodes on the finest mesh. It is shown that the local multilevel methods are optimal, i.e., the convergence rate of the multilevel methods is independent of the mesh sizes and mesh levels. Numerical experiments are given to confirm the theoretical results.

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Author:Xuejun Xu, Huangxin Chen, Ronald H. W. HoppeORCiDGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1294
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2009-21)
Publishing Institution:Universität Augsburg
Contributing Corporation:University of Houston, Chinese Academy of Sciences
Release Date:2009/08/14
Tag:local multilevel methods; adaptive nonconforming finite element methods; convergence analysis; optimality
GND-Keyword:Elliptisches Randwertproblem; Finite-Elemente-Methode; Mehrebenenoptimierung; Konvergenz
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand