Numerische Mathematik

, Volume 16, Issue 4, pp 322–333

Error-bounds for finite element method

  • Ivo Babuška
Article

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References

  1. 1.
    Nečas, J.: Sur la coercivité des formes sesquilinéaires elliptiques. Rev. Roumaine de Math. Pure et App.9, No. 1, 47–69 (1964).Google Scholar
  2. 2.
    —— Sur une méthode pour résoudre les equations dérivées partielles du type elliptique voisine de la variationnelle. Ann. Sc. Norm. Sup., Pisa, Ser. III,16, 4, 305–326 (1962).Google Scholar
  3. 3.
    Nirenberg, L.: Remarks on strongly elliptic partial differential equations. Comm. Pure App. Math.8, 649–675 (1955).Google Scholar
  4. 4.
    Kantorovich, L. V., Akilov, G. P.: Functional analyses in normed spaces [translated from Russian]. New York: McMillan Press 1964.Google Scholar
  5. 5.
    Aronszajn, H.: Boundary value of function with finite Dirichlet integral. Conference on Partial Differential Equations Studies in Eigenvalue Problems, No. 14, University of Kansas, 1955.Google Scholar
  6. 6.
    Slobodeckii, M. I.: Generalized Sobolev spaces and their application to boundary problems for partial differential equations. Leningr. gos. Univ.197, 54–112 (1958).Google Scholar
  7. 7.
    Lions, J. L., Magenes, E.: Problèmes aux limites non homogèènes. IV. Ann. Se. Norm. Sup. Pisa, Ser. III,15, 4, 311–326 (1961).Google Scholar
  8. 8.
    —, — Problèmes aux limites non homogènes. Paris: Dunod 1968.Google Scholar
  9. 9.
    Krein, S. G., Petunin, Yu. I.: Scales of Banach spaces. Russian Math. Surveys21, No. 2, 85–160 (1966).Google Scholar
  10. 10.
    Babuška, L : Approximation by the hill functions. To appear. Technical Note BN-648, 1970, University of Maryland, Institute for Fluid Dynamics and Applied Mathematics. To appear in CMUC.Google Scholar
  11. 11.
    Laasonen, P.: On the degree of convergence of discrete approximation for the solution of the Dirichlet problem. Ann. Acad. Sci. Finn. Ser. A,I, No. 246 (1957)Google Scholar
  12. 12.
    —— On the truncation error of discrete approximations into the solution of Dirichlet problems in a domain with corners. J. Assoc. Comp. Math.5, 32–38 (1958)Google Scholar
  13. 13.
    Veidinger, L.: On the order of convergence of finite difference approximations to the solution of the Dirichlet problem in a domain with corners. Studia Scient. Math. Hung.3, No. 1-3, 337–343 (1968).Google Scholar
  14. 14.
    Ciarlet, P.: Discrete variational Green's function. To appear.Google Scholar
  15. 15.
    Babuška, I., Práger, M., Vitásek, E.: Numerical processes in differential equations. New York: J. Wiley 1966.Google Scholar
  16. 16.
    Volkov, E. A.: Method of composit meshes for bounded and unbounded domain with piecewise smooth boundary (in Russian). Proceedings of the Steklov institute of Mathematics No. 96, 117–148 (1968).Google Scholar
  17. 17.
    Babuška, L : The rate of convergence for the finite element method. Technical Note BN-646, 1970, University of Maryland, Institute for Fluid Dynamics and Applied Mathematics. To appear in SIAM J. Num. Anal.Google Scholar
  18. 18.
    — Finite element method for domains with corners. Technical Note BN-636, 1970, University of Maryland, Institute for Fluid Dynamics and Applied Mathematics. To appear in Computing.Google Scholar
  19. 19.
    — The finite element method for elliptic equations with discontinuous coefficients. Technical Note BN-631, 1969, University of Maryland, Institute for Fluid Dynamics and Applied Mathematics. To appear in Computing.Google Scholar
  20. 20.
    — The finite element method for elliptic differential equations. Technical Note Note BN-653, 1970, University of Maryland, Institute for Fluid Dynamics and Applied Mathematics. To appear in SYNSPADE Proceedings (Symposium on the Numerical Solution Solution of Partial Differential Equations), May 11–15, 1970, University of Maryland.Google Scholar
  21. 21.
    — Computation of derivatives in the finite element method. Technical Note BN-650, 1970, University of Maryland, Institute for Fluid Dynamics and Applied Mathematics. To appear in CMUC.Google Scholar
  22. 22.
    — 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.Google Scholar
  23. 23.
    — The finite element method for unbounded domains I. Technical Note BN-670, 1970, University of Maryland, Institute for Fluid Dynamics and Applied Mathematics.Google Scholar

Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • Ivo Babuška
    • 1
  1. 1.University of MarylandInstitute for Fluid Dynamics and Applied MathematicsCollege ParkUSA

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