Skip to main content
SpringerLink
Log in

A finite element scheme for domains with corners

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

Abstract

This paper is concerned with the rate of convergence of the finite element method on polygonal domains in weighted Sobolev spaces. It is shown that the use of different spaces of trial and test functions will restrict the usual low rate of convergence to a neighborhood of each vertex of the polygonal domain.L 2-convergence and lower bounds on the error are also studied.

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

Similar content being viewed by others

References

  1. Babuška, I.: The finite element method for elliptic equations with discontinuous coefficients. Computing5, 207–213 (1970).

    Google Scholar 

  2. Babuška, I.: Error-bounds for finite element method. Num. Math.16, 322–333 (1971).

    Google Scholar 

  3. Babuška, I.: Computation of derivatives in the finite element method. Commentations Mathematicae Universitates Carolinae [CMUC]11, 3, 545–558 (1970).

    Google Scholar 

  4. Babuška, I.: Approximation by Hill functions. CMUC11, 4, 787–811 (1970).

    Google Scholar 

  5. Babuška, I.: The finite element method for elliptic differential equations, Numerical solution of partial differential equations II. SYNSPADE 1970, Edited by B. Hubbard. New York-London: Academic Press 1971, 69–107.

    Google Scholar 

  6. Babuška, I.: Finite element method for domains with corners. Computing6, 264–273 (1970).

    Google Scholar 

  7. Babuška, I.: A Remark to the finite element method. CMUC12, 2, 367–376 (1971).

    Google Scholar 

  8. Babuška, I.: The rate of convergence for the finite element method. SIAM J. Num. Anal.8, 2, 304–315 (1971).

    Article  Google Scholar 

  9. Babuška, I.: The finite element method for infinite domains I. Math. of Comp.117, 1–11 (1972).

    Google Scholar 

  10. Babuška, I.: Approximation by hill functions II. CMUC13, 1, 1–22 (1972).

    Google Scholar 

  11. Babuška, I.: Finite element method with penalty, technical note BN-710, 1971, University of Maryland, Institute for Fluid Dynamics and Applied Mathematics.

  12. Babuška, I., Segethová, J., Segeth, K.: Numerical experiments with finite element method I, technical note BN-669, 1970, University of Maryland, Institute for Fluid Dynamics and Applied Mathematics.

  13. Bramble, J. H., Schatz, A. H.: On the numerical solution of elliptic boundary value problems by least square approximation data. SYNSPADE 1970, Academic Press 1971, 107–133.

  14. Felippa, C., Clough, R. W.: The finite element method in solid mechanics. SIAM-AMS Proceeding, AMS, Providence, Rhode Island 1970, editor G. Birkhoff and R. S. Varga, p. 210–252.

  15. George, J. A.: Computer implementation of the finite element method. Stanford University, Comp. Sci. Dept., Rep., Stan-cs-71-208, 1971.

  16. Kondrat'ev, V. A.: Boundary value problems for elliptic equations in domains with comcal or angular points [in Russian]. Proc. of the Moscow Math. Soc., v. 16, 1967, 209–292.

    Google Scholar 

  17. Kufner, A.: Einige Eigenschaften der Sobolevschen Räume mit Belegungsfunktion. Czechoslovak Math. Journal15, 597–620 (1961).

    Google Scholar 

  18. Marcal, P. T.: On general purpose programs for finite element analysis with special reference to geometric and material nonlinearities. SYNSPADE 1970, Academic Press, 1971, 433–469.

  19. Nečas, J.: Les méthodes directes en théorie équations elliptiques. Prague, Academia, 1971.

    Google Scholar 

  20. Nečas, J.: Sur la coercivité des formes sesquilinéares elliptiques. Rer Roumaine de math. Pure et App.9, 47–69 (1964).

    Google Scholar 

  21. Strang, G.: The finite element method and approximation theory. SYNSPADE 1970, Academic Press, 1971.

  22. Strang, G., Fix, G.: An analysis of the finite element method. To appear.

  23. Turner, M. J., Clough, R. W., Martin, H. C., Topp, L. J.: Stiffness and deflection analysis of complex structures. J. Aeronautical Sci.23, 805–823 (1956).

    Google Scholar 

  24. Zienkiewicz, O. C.: The finite element method in structural and continuum mechanics. New York: McGraw Hill.

  25. Zlámal, M.: On finite element method. Num. Math.12, 394–409 (1968).

    Google Scholar 

  26. Zlámal, M.: On some finite procedures for solving second order boundary value problems. Num. Math.14, 42–48 (1969).

    Google Scholar 

  27. Zenišek, A.: Interpolation polynomials on the triangle. Num. Math.15, 283–296 (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Fluid Dynamics & Applied Mathematics, University of Maryland, 20742, College Park, Maryland, USA

    Ivo Babuška

  2. U.S. Naval Academy, 21402, Annapolis, Maryland, USA

    Michael B. Rosenzweig

Authors
  1. Ivo Babuška
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael B. Rosenzweig
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by the Atomic Energy Commission under contract no. AEC AT-(40-1)-3443/4.

This research was supported in part by the U.S. Naval Academy Research Council.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Babuška, I., Rosenzweig, M.B. A finite element scheme for domains with corners. Numer. Math. 20, 1–21 (1972). https://doi.org/10.1007/BF01436639

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01436639

Keywords

Search

Navigation