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Reliable Computing

, Volume 3, Issue 3, pp 297–303 | Cite as

Two-sided Multigrid Method for Elliptic Boundary Value Problems

  • Boris S. Dobronets
Article
  • 13 Downloads

Abstract

We consider a two-sided method for solving elliptic boundary value problems. On a sequence of grids the special function s is formed. On every grid the function s is refined to minimize the defect. Using the function s and the principle of monotonicity, the boundaries of exact solution s, s are constructed.

Keywords

Mathematical Modeling Exact Solution Computational Mathematic Industrial Mathematic Special Function 
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References

  1. 1.
    Dobronets, B. S.: Numerical Methods Using Defects, Reliable Computing 1 (4) (1995), pp. 383–391.Google Scholar
  2. 2.
    Dobronets, B. S.: A Posteriori Error Estimation for Partial Differential Equations, in: Alefeld, G., Frommer, A., and Lang, B. (eds), Scientific Computation and Validated Numerics, Akademie-Verlag, Berlin, 1996, pp. 239–244.Google Scholar
  3. 3.
    Dobronets, B. S. and Shaidurov, V. V.: Two-Sided Numerical Methods, Nauka (Siberian Department), Novosibirsk, 1990 (in Russian).Google Scholar
  4. 4.
    Shaidurov, V. V.: Multigrid Methods of Finite Elements, Nauka, Moscow, 1989 (in Russian).Google Scholar
  5. 5.
    Strang, G. and Fix, G. J.: An Analysis of the Finite Element Method, Englewood Cliffs, Prentice-Hall, 1973.Google Scholar
  6. 6.
    Varga, R.: Functional Analysis and Approximation Theory in Numerical Analysis, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1971.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Boris S. Dobronets
    • 1
  1. 1.Krasnoyarsk State Technical UniversityKrasnoyarskRussia

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