On the accuracy of multigrid truncation error estimates.
Fulton, Scott R. (2003)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
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Displaying similar documents to “Multigrid for the Wilson mortar element method.”
On the accuracy of multigrid truncation error estimates.
Minimization of functional majorant in a posteriori error analysis based on (div) multigrid-preconditioned CG method.
Valdman, Jan (2009)
Advances in Numerical Analysis
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A multilevel preconditioner for the mortar method for nonconforming finite element
Talal Rahman, Xuejun Xu (2009)
ESAIM: Mathematical Modelling and Numerical Analysis
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A multilevel preconditioner based on the abstract framework of the auxiliary space method, is developed for the mortar method for the nonconforming finite element or the lowest order Crouzeix-Raviart finite element on nonmatching grids. It is shown that the proposed preconditioner is quasi-optimal in the sense that the condition number of the preconditioned system is independent of the mesh size, and depends only quadratically on the number of refinement levels. Some...
A finite element method for domain decomposition with non-matching grids
Roland Becker, Peter Hansbo, Rolf Stenberg (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this note, we propose and analyse a method for handling interfaces between non-matching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson’s equation as a model. A priori and a posteriori error estimates are given. Some numerical results are included.
Local error estimates and adaptive refinement for first-order system least squares (FOSLS).
Berndt, Markus, Manteuffel, Thomas A., McCormick, Stephen F. (1997)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
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Pointwise a posteriori error analysis for an adaptive penalty finite element method for the obstacle problem.
French, Donald A., Larsson, Stig, Nochetto, Ricardo H. (2001)
Computational Methods in Applied Mathematics
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A short philosophical note on the origin of smoothed aggregations
Fraňková, Pavla, Hanuš, Milan, Kopincová, Hana, Kužel, Roman, Vaněk, Petr, Vastl, Zbyněk
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We derive the smoothed aggregation two-level method from the variational objective to minimize the final error after finishing the entire iteration. This contrasts to a standard variational two-level method, where the coarse-grid correction vector is chosen to minimize the error after coarse-grid correction procedure, which represents merely an intermediate stage of computing. Thus, we enforce the global minimization of the error. The method with smoothed prolongator is thus interpreted...
Convergence and quasi-optimal complexity of a simple adaptive finite element method
Roland Becker, Shipeng Mao (2009)
ESAIM: Mathematical Modelling and Numerical Analysis
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We prove convergence and quasi-optimal complexity of an adaptive finite element algorithm on triangular meshes with standard mesh refinement. Our algorithm is based on an adaptive marking strategy. In each iteration, a simple edge estimator is compared to an oscillation term and the marking of cells for refinement is done according to the dominant contribution only. In addition, we introduce an adaptive stopping criterion for iterative solution which compares an estimator for the iteration...
Space adaptive finite element methods for dynamic obstacle problems.
Blum, Heribert, Rademacher, Andreas, Schröder, Andreas (2008)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
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Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes.
Chan, Tony F., Smith, Barry F. (1994)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
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A parallel multigrid method using the full domain partition.
Mitchell, William F. (1997)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
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Algebraic domain decomposition solver for linear elasticity
Aleš Janka (1999)
Applications of Mathematics
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We generalize the overlapping Schwarz domain decomposition method to problems of linear elasticity. The convergence rate independent of the mesh size, coarse-space size, Korn’s constant and essential boundary conditions is proved here. Abstract convergence bounds developed here can be used for an analysis of the method applied to singular perturbations of other elliptic problems.