Skip to main content
SpringerLink
Log in

Accuracy of the penalty method for parabolic variational inequalities with an obstacle inside the domain

  • Published:
Russian Mathematics Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. A. Friedman, Variational Principles and Free Boundary Problems (Wiley-Interscience, New York, 1982; Mir,Moscow, 1990).

    MATH  Google Scholar 

  2. F. Donati, “A Penalty Method Approach to Strong Solutions of Some Nonlinear Parabolic Unilateral Problems,” Nonlinear Anal. 6, 585–597 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  3. R. Glowinski, J.-L. Lions, and R. Trémolières, Numerical Analysis of Variational Inequalities (North-Holland Publishing Company, Amsterdam, 1981; Mir, Moscow, 1979).

    MATH  Google Scholar 

  4. M. Boman, A Posteriori Error Analysis in the Maximum Norm for a Penalty Finite Element Method for the Time-Dependent Obstacle Problem (Chalmers University of Technology and Goteborg University, Amsterdam, 2000).

    Google Scholar 

  5. R. Scholz, “Numerical Solution of the Obstacle Problem by the Penalty Method,” II. Time-Dependent Problems Numer. Math. 49, 255–268 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. Bensoussan and J.-L. Lions, Impulse Control and Quasivariational Inequalities (Gauthiers-Villers, Bordas, Paris, 1984; Nauka, Moscow, 1987).

    Google Scholar 

  7. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications (Academic Press, New York, 1980; Mir, Moscow, 1983).

    MATH  Google Scholar 

  8. D. E. Apushkinskaya, N. N. Ural’tseva, and H. Shahgholian, “Lipschitz Property of the Free Boundary in the Parabolic Obstacle Problem,” St. Petersburg Math. J., No. 15, 375–391 (2004).

  9. R. Z. Dautov, “Exact Penalty Operators for Elliptic Variational Inequalities with an Obstacle Inside the Domain,” Differents. Uravneniya 31(6), 1008–1017 (1995).

    MathSciNet  MATH  Google Scholar 

  10. R. Z. Dautov, “A Problem with an Obstacle Inside the Domain. Approximate Definition of a Free Boundary,” TrudyMatem. Tsentra in. N. I. Lobachevskogo 2, 121–170 (1999).

    Google Scholar 

  11. H. Gajewski, K. Gröger, and K. Zacharias, Nonlinear Operator Equations and Operator Differential Equations (Akademie Verlag, Berlin, 1974; Mir, Moscow, 1978).

    Google Scholar 

  12. M. C. Palmeri, “Homographic Approximation for Some Nonlinear Parabolic Unilateral Problems,” J. Convex Anal. 7(2), 353–373 (2000).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kazan State University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    A. I. Mikheeva & R. Z. Dautov

Authors
  1. A. I. Mikheeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Z. Dautov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. I. Mikheeva.

Additional information

Original Russian Text © A.I. Mikheeva, R.Z. Dautov, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 2, pp. 41–47.

About this article

Cite this article

Mikheeva, A.I., Dautov, R.Z. Accuracy of the penalty method for parabolic variational inequalities with an obstacle inside the domain. Russ Math. 52, 39–45 (2008). https://doi.org/10.3103/S1066369X08020060

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X08020060

Keywords

Search

Navigation