Article PDF
Avoid common mistakes on your manuscript.
References
Nečas, J.: Sur la coercivité des formes sesquilinéaires elliptiques. Rev. Roumaine de Math. Pure et App.9, No. 1, 47–69 (1964).
—— 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).
Nirenberg, L.: Remarks on strongly elliptic partial differential equations. Comm. Pure App. Math.8, 649–675 (1955).
Kantorovich, L. V., Akilov, G. P.: Functional analyses in normed spaces [translated from Russian]. New York: McMillan Press 1964.
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.
Slobodeckii, M. I.: Generalized Sobolev spaces and their application to boundary problems for partial differential equations. Leningr. gos. Univ.197, 54–112 (1958).
Lions, J. L., Magenes, E.: Problèmes aux limites non homogèènes. IV. Ann. Se. Norm. Sup. Pisa, Ser. III,15, 4, 311–326 (1961).
—, — Problèmes aux limites non homogènes. Paris: Dunod 1968.
Krein, S. G., Petunin, Yu. I.: Scales of Banach spaces. Russian Math. Surveys21, No. 2, 85–160 (1966).
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.
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)
—— 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)
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).
Ciarlet, P.: Discrete variational Green's function. To appear.
Babuška, I., Práger, M., Vitásek, E.: Numerical processes in differential equations. New York: J. Wiley 1966.
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).
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.
— 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.
— 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.
— 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.
— 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.
— 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.
— The finite element method for unbounded domains I. Technical Note BN-670, 1970, University of Maryland, Institute for Fluid Dynamics and Applied Mathematics.
Author information
Authors and Affiliations
Additional information
Dedicated to Professor L. Collatz on his 60th birthday
This work was supported in part by National Science Foundation Grant NSF-GP 7844.
Rights and permissions
About this article
Cite this article
Babuška, I. Error-bounds for finite element method. Numer. Math. 16, 322–333 (1971). https://doi.org/10.1007/BF02165003
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02165003