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Numerische Mathematik

, Volume 58, Issue 1, pp 231–242 | Cite as

On an iterative method for variational inequalities

  • A. Pitonyak
  • P. Shi
  • M. Shillor
Article

Summary

A number of numerical solutions are presented as examples of a new iterative method for variational inequalities. The iterative method is based on the reduction of variational inequalities to the Wiener-Hopf equations. For obstacle problems the convergence is guaranteed inW1,p spaces forp≧2. The examples presented are one and two dimensional obstacle problems in cases when the Greens function is known, but the method is very general.

Subject classifications

AMS (MOS): 65N30 CR: G1.8 

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References

  1. [BC] C. Baiocchi, A. Capelo: Variational and quasivariational inequalities. Chichester: Wiley 1984Google Scholar
  2. [EO] C.M. Elliott, J.R. Ockendon: Weak and variational methods for moving boundary problems. London: Pitman 1982Google Scholar
  3. [G] R. Glowinski: Finite-element methods for variational inequalities. In: Kardestuncer E. (ed.) Finite element handbook, pp. 1.219–1.253. New York: McGraw-Hill 1987Google Scholar
  4. [GTL] R. Glowinski, J.L. Lions, R. Trémolières: Numerical analysis of variational inequalities. Amsterdam: North-Holland 1981Google Scholar
  5. [K] H. Kardestuncer: Finite element handbook, New York: McGraw-Hill 1987Google Scholar
  6. [KO] N. Kikuchi, J.T. Oden: Contact problems in elasticity: a study of variational inequalities and finite element methods. Philadelphia: SIAM 1988Google Scholar
  7. [KS] D. Kinderlehrer, G. Stampacchia: An introduction to variational inequalities and their applications. New York: Academic Press 1980Google Scholar
  8. [S1] P. Shi: Equivalence of variational inequalities with Wiener-Hopf equations. Proceedings of AMS (to appear)Google Scholar
  9. [S2] P. Shi: An interative method for obstacle problems via Green's functions.Nonlin. Anal. TMA (to appear)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • A. Pitonyak
    • 1
  • P. Shi
    • 1
  • M. Shillor
    • 1
  1. 1.Department of Mathematical SciencesOakland UniversityRochesterUSA

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