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An approximate waves-bordering algorithm for adaptive finite elements analysis. (English)
Numer. Algorithms 21, No.1-4, 311-322 (1999).
The authors present a solution method for linear equations generated from a sequence of finite element meshes. The method assumes that each mesh in the sequence is largely the same as the previous mesh and that the changed portions are localized, as would be the case when a mesh is adaptively updated based on error estimates. The method is based loosely on work of {\it C. Brezinski, M. Morandi Checchi} and {\it M. Redivo-Zaglia} [SIAM J. Matrix Anal. Appl. 15, No. 3, 922-937 (1994; Zbl 0812.65017)] but is tailored for the case at hand. The solution method is briefly summarized in this paper, with details presented in a forthcoming companion paper. Unfortunately, the current paper does not contain sufficient detail to evaluate the method or its applicability. Neither are conditions described under which breakdown does not occur, nor are error estimates provided to establish the validity of the approximate waves-bordering algorithm. A numerical example is presented whose results indicate the potential of the algorithm when the number of mesh nodes is little changed from an earlier mesh.
Reviewer: Myron Sussman (Bethel Park)
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