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Local and parallel finite element algorithms based on two-grid discretizations

Authors: Jinchao Xu and Aihui Zhou
Journal: Math. Comp. 69 (2000), 881-909
MSC (1991): Primary 65N15, 65N30, 65N55, 65F10
Published electronically: May 19, 1999
MathSciNet review: 1654026
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Abstract: A number of new local and parallel discretization and adaptive finite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems. These algorithms are motivated by the observation that, for a solution to some elliptic problems, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. The theoretical tools for analyzing these methods are some local a priori and a posteriori estimates that are also obtained in this paper for finite element solutions on general shape-regular grids. Some numerical experiments are also presented to support the theory.

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Additional Information

Jinchao Xu
Affiliation: Center for Computational Mathematics and Applications, Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802

Aihui Zhou
Affiliation: Institute of Systems Science, Academia Sinica, Beijing 100080, China

Keywords: Adaptive, finite elements, local a priori and a posteriori error estimates, nonsymmetric, parallel algorithm, two-grid method
Received by editor(s): July 21, 1998
Published electronically: May 19, 1999
Additional Notes: This work was partially supported by NSF DMS-9706949, NSF ACI-9800244 and NASA NAG2-1236 through Penn State and Center for Computational Mathematics and Applications, The Pennsylvania State University.
Article copyright: © Copyright 2000 American Mathematical Society

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