Summary
The rate of convergence of the finite element method is greatly influenced by the existence of corners on the boundary. The paper shows that proper refinement of the elements around the corners leads to the rate of convergence which is the same as it would be on domain with smooth boundary.
Zusammenfassung
Die Konvergenzgeschwindigkeit der Methode der endlichen Elemente wird grundsätzlich durch die Ecken der Grenze beeinflußt. In der Arbeit wird gezeigt, daß man durch geeignetes Verfeinern in der Umgebung der Ecken dieselbe Konvergenz der Methode der endlichen Elemente erzielen kann, wie im Falle eines Gebietes mit glatter Grenze.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Volkov, E. A.: Method of composit meshes for bounded and unbounded domain with piecewise smooth boundar (in Russian). Proc. of the Steklov Institute of Math.96, 117–148 (1968).
Laasonen, P.: On the degree of convergence of discrete approximation for the solution of theDirichlet problem. Ann. Acad. Sci. Finn., Ser. A,I, 246 (1957).
Laasonen, P.: On the truncation error of discrete approximations into the solution ofDirichlet problems in a domain with corners. Journal Assoc. Comp. Math.5, 32–38 (1958).
Lions, J. L., andE. Magenes: Problèms aux limites non homogènes. Paris: Dunod. 1968.
Krejn, S. G., andYu I. Petunin: Scales ofBanach Spaces. Russian Math. Surveys21, 85–160 (1966).
Deny, J., andJ. L. Lions: Les espaces du type deBeppo Levi. Ann. de l'Inst. FourierV, 305–370 (1953/54).
Hardy, G. H., J. E. Littlewood, andG. Polya: Inequalities. Cambridge. 1964.
Stein, E.: Lectures Notes. Orsay, 1966/67. Tech. Note BN-648, April 1970. Inst. for Fluid Dyn., University of Maryland.
Babuška, I.: Approximation by hill functions. To appear in CMUC Prague.
Nečas, J.: Les méthodes directes en théorie des équations elliptiques. Prague: Academia. 1967.
Babuška, I.: Error-Bounds for Finite Element Method. Tech. Note BN-630. November 1969. Inst. for Fluid Dyn., University of Maryland. To appear in Num. Math.
Kondrat'ev, V. A.: Boundary values problems for elliptical equations on the domains with cones (in Russian). Proc. of the Moscow Math. Soc. V.16, 209–292 (1967).
Laasonen, P.: On the behavior of the solution of theDirichlet problem at analytic corners. Ann. Acad. Sc. Fennicale, Ser. A,I, 241 (1947).
Uspenskij, S. V.: The embeddings theorems for the weight classes, Moscow: Proc. of the Steklov Inst.,60 (1961).
Babuška, I.: The rate of Convergence for the Finite Element Method. Tech. Note BN-646, March 1970. Inst. for Fluid Dyn., University of Maryland. To appear in SIAM Journal, Num. Math.
Babuška I.: The Finite Element Method for Elliptic Differential Equations. Tech. Note BN-653. May 1970. Inst. for Fluid Dyn., University of Maryland. To appear in SYNSPADE. 1970. (B. E. Hubbard editor),
Author information
Authors and Affiliations
Additional information
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. Finite element method for domains with corners. Computing 6, 264–273 (1970). https://doi.org/10.1007/BF02238811
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02238811