The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids
type: Item
instance of: scholarly article
title: The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids
zbMATH Open document ID: 0857.65129
DOI: 10.1007/BF02238513
published in: Computing
publication date: 1997-03-09T00:00:00Z
review text: For the numerical solution of elliptic boundary value problems discretized by finite element schemes on unstructured grids the author develops an abstract framework of the auxiliary space method. This is an optimal preconditioning technique that results from the proper combination of an appropriate smoother and a structured auxiliary grid and can be interpreted as a two-level nonnested multigrid preconditioner. Examples include the use of a -- nested coarse grid space as an auxiliary space, -- lower-order element as an auxiliary space for a higher-order element, -- conforming element as an auxiliary space for a nonconforming element.
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 878404
zbMATH Keywords: auxiliary space method
zbMATH Keywords: finite element
zbMATH Keywords: unstructured grids
zbMATH Keywords: optimal preconditioning
zbMATH Keywords: multigrid
author: Jinchao Xu
reviewed by: R. H. W. Hoppe
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 878404