Skip to main content
Log in

Two-sided Multigrid Method for Elliptic Boundary Value Problems

  • Published:
Reliable Computing

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Dobronets, B. S.: Numerical Methods Using Defects, Reliable Computing 1 (4) (1995), pp. 383–391.

    Google Scholar 

  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. Dobronets, B. S. and Shaidurov, V. V.: Two-Sided Numerical Methods, Nauka (Siberian Department), Novosibirsk, 1990 (in Russian).

    Google Scholar 

  4. Shaidurov, V. V.: Multigrid Methods of Finite Elements, Nauka, Moscow, 1989 (in Russian).

    Google Scholar 

  5. Strang, G. and Fix, G. J.: An Analysis of the Finite Element Method, Englewood Cliffs, Prentice-Hall, 1973.

    Google Scholar 

  6. Varga, R.: Functional Analysis and Approximation Theory in Numerical Analysis, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dobronets, B.S. Two-sided Multigrid Method for Elliptic Boundary Value Problems. Reliable Computing 3, 297–303 (1997). https://doi.org/10.1023/A:1009983126109

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009983126109

Keywords