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Fast Adaptive Composite Grid (FAC) Methods: Theory for the Variational Case

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Defect Correction Methods

Part of the book series: Computing Supplementum ((COMPUTING,volume 5))

Abstract

The subject of this paper is the fast adaptive composite grid (FAC) method for solving variationally posed differential boundary value problems. Related to local defect corrections (LDC) and multilevel adaptive techniques (MLAT), an important difference is that FAC forces the user to specify the discrete problem on the finest composite grid — it is not rather an implicit result of the adaptive process. The advantages are that FAC can more readily meet practical objectives, does not suffer from some of the practical limitations of (“natural”) versions of LDC and MLAT, and lends itself to a simple theory. The latter is the subject of this paper.

This work was supported by AFOSR grant number FQ8671-83-01322, the Gesellschaft für Datenverarbeitung, and the National Bureau of Standards.

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References

  1. Bai, D., Brandt, A.: Local mesh refinement multilevel techniques. Research report, Dept. Appl. Math., Weizmann Inst. Sci., Rehovot, Israel, 1983.

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  2. Hackbusch, W.: Domain decomposition techniques. (This publication.)

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  3. McCormick, S.: A variational theory for multilevel adaptive techniques (MLAT). Proc. Multigrid Conf., Bristol, Sept. 1983, IMA (to appear).

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  4. McCormick, S.: Multigrid methods for variational problems: III. Research report, Dept. Math., Colorado State University, Sept. 1983.

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  5. McCormick, S.: Multigrid methods for variational problems. SIAM J. Numer. Anal. 19, 924–929 (1982).

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Author information

Authors and Affiliations

  1. Department of Mathematics, Colorado State University, Fort Collins, CO, 80523, USA

    Prof. Dr. S. McCormick

Authors
  1. Prof. Dr. S. McCormick
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik, Universität Marburg, Federal Republic of Germany

    Klaus Böhmer

  2. Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Austria

    Hans J. Stetter

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© 1984 Springer-Verlag

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McCormick, S. (1984). Fast Adaptive Composite Grid (FAC) Methods: Theory for the Variational Case. In: Böhmer, K., Stetter, H.J. (eds) Defect Correction Methods. Computing Supplementum, vol 5. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7023-6_7

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  • DOI: https://doi.org/10.1007/978-3-7091-7023-6_7

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81832-9

  • Online ISBN: 978-3-7091-7023-6

  • eBook Packages: Springer Book Archive

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