The Rate of Convergence for the Finite Element Method

Abstract

Previous article Next article The Rate of Convergence for the Finite Element MethodIvo BabuškaIvo Babuškahttps://doi.org/10.1137/0708031PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe character of the proper refinement of the elements (mesh) around the boundary is studied. It is shown that it is possible to obtain the highest (optimal) rate of convergence by this refinement.[1] H. Aronszajn, Boundary value of functions with finite Dirichlet integral, Conference on Partial Differential Equations, No. 14, University of Kansas, Lawrence, 1955 0068.08201 Google Scholar[2] M. I. Slobodeckii, Generalized Sobolev spaces and their application to boundary problems for partial differential equations, Amer. Math. Soc. Transl. (2), 57 (1966), 207–275 0192.22801 Google Scholar[3] J.-L. Lions and , E. Magenes, Problèmes aux limites non homogènes et applications. 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Zienkiewicz, The Finite Element Method in Structural and Continuum Mechanics, McGraw-Hill, London, 1967 0189.24902 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Numerical Simulation of Vehicle–Lighting Pole Crash Tests: Parametric Study of Factors Influencing Predicted Occupant Safety Levels25 May 2021 | Materials, Vol. 14, No. 11 Cross Ref A phase-field model for fractures in nearly incompressible solids24 July 2019 | Computational Mechanics, Vol. 65, No. 1 Cross Ref Computable Error Estimates for Finite Element Approximations of Elliptic Partial Differential Equations with Rough Stochastic DataEric Joseph Hall, Håkon Hoel, Mattias Sandberg, Anders Szepessy, and Raúl Tempone8 December 2016 | SIAM Journal on Scientific Computing, Vol. 38, No. 6AbstractPDF (1386 KB)Topological object types for morphodynamic modeling languages Cross Ref Well-posedness and Regularity for the Elasticity Equation with Mixed Boundary Conditions on Polyhedral Domains and Domains with Cracks21 October 2008 | Archive for Rational Mechanics and Analysis, Vol. 195, No. 1 Cross Ref Improving the Rate of Convergence of High-Order Finite Elements on Polyhedra II: Mesh Refinements and InterpolationNumerical Functional Analysis and Optimization, Vol. 28, No. 7-8 Cross Ref Weighted Sobolev spaces and regularity for polyhedral domainsComputer Methods in Applied Mechanics and Engineering, Vol. 196, No. 37-40 Cross Ref Finite element approximations forΔu −qu = f on a Riemann surfaceJapan Journal of Industrial and Applied Mathematics, Vol. 19, No. 1 Cross Ref The Approximation Problem for Drift-Diffusion SystemsJoseph W. 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Cross Ref FINITE ELEMENT APPLICATIONS IN MATHEMATICAL PHYSICS Cross Ref The finite element method with penalty1 January 1973 | Mathematics of Computation, Vol. 27, No. 122 Cross Ref A finite element scheme for domains with cornersNumerische Mathematik, Vol. 20, No. 1 Cross Ref RATE OF CONVERGENCE OF THE FINITE ELEMENT METHOD Cross Ref The finite element method for infinite domains. I1 January 1972 | Mathematics of Computation, Vol. 26, No. 117 Cross Ref Volume 8, Issue 2| 1971SIAM Journal on Numerical Analysis History Submitted:23 April 1970Published online:14 July 2006 InformationCopyright © 1971 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0708031Article page range:pp. 304-315ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics