Skip to main content
Log in

Estimation of convergence rate of different solutions to generalized solution of dirichlet problem for helmholtz equation of class\(\mathop W\limits^0 \) 2 1(Ω) in convex domain

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

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

Access this article

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

Instant access to the full article PDF.

Literature cited

  1. S. A. Voitsekhovskii, V. L. Makarov, A. A. Samarskii, and T. G. Shablii, “On convergence rate estimate for difference solutions to generalized solution of Dirichlet problem for Helmholtz equations in convex polygon,” Dokl. Akad. Nauk SSSR,273, No. 5, 1040–1044 (1983).

    Google Scholar 

  2. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press (1968).

  3. I. Nechas, “On solution of second-order partial elliptic differential equations with unbounded Dirichlet integral,” Chekhosl. Mat. Zh.,10, No. 2, 283–298 (1960).

    Google Scholar 

  4. L. A. Oganesyan and L. A. Rukhovets, Variational Difference Methods for Solving Elliptic Equations [in Russian], Izd. Akad. Nauk ArmSSR, Erevan (1979).

    Google Scholar 

  5. J. H. Bramble, T. Duport, and V. Thomee, “Projection methods for Dirichlet's problem in approximating polygonal domains with boundary value corrections,” Math. Comp.,27, No. 120, 869–879 (1972).

    Google Scholar 

  6. V. L. Makarov and A. A. Samarskii, “Application of exact difference schemes to estimating convergence rate of method of straight lines,” Zh. Vychisl. Mat. Mat., Fiz.,20, No. 2, 381–397 (1980).

    Google Scholar 

  7. M. Dryya, “A priori estimates in W2 2 in convex domain for systems of elliptic difference equations,” ibid.,12, No. 6, 1595–1601 (1972).

    Google Scholar 

  8. J. H. Bramble and S. R. Hilbert, “Bounds for a class of linear functionals with applications to Hermite interpolation,” Numer. Math.,16, No. 4, 362–369 (1971).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 38, No. 1, pp. 98–101, January–February, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Voitsekhovskii, S.A., Marakov, V.L. & Shablii, T.G. Estimation of convergence rate of different solutions to generalized solution of dirichlet problem for helmholtz equation of class\(\mathop W\limits^0 \) 2 1(Ω) in convex domain. Ukr Math J 38, 88–90 (1986). https://doi.org/10.1007/BF01056766

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01056766

Keywords

Navigation