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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Local and parallel finite element algorithms based on two-grid discretizations
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by Jinchao Xu and Aihui Zhou HTML | PDF
Math. Comp. 69 (2000), 881-909 Request permission


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
  • MR Author ID: 228866
  • Email:
  • Aihui Zhou
  • Affiliation: Institute of Systems Science, Academia Sinica, Beijing 100080, China
  • Email:
  • 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.
  • © Copyright 2000 American Mathematical Society
  • Journal: Math. Comp. 69 (2000), 881-909
  • MSC (1991): Primary 65N15, 65N30, 65N55, 65F10
  • DOI:
  • MathSciNet review: 1654026