Accession Number : ADA140952
Title : The Approximation Theory for the P-Version of the Finite Element Method. II.
Descriptive Note : Final rept.,
Corporate Author : MARYLAND UNIV COLLEGE PARK LAB FOR NUMERICAL ANALYSIS
Personal Author(s) : Dorr,M R
PDF Url : ADA140952
Report Date : Apr 1984
Pagination or Media Count : 44
Abstract : In Part II of this paper, the approximation theory developed in Part I is used to determine the piecewise polynomial approximability of solutions of elliptic problems on polygonal domains in R2 and polyhedra in R3. From these estimates, convergence orders for the p-version of the finite element method applied to such problems are readily obtained. The critical issue is the approximation of the singularities which occur at the non-smooth parts of the domain boundaries. Numerical results for two problems from two-dimensional linear elasticity are also presented. The computations show that the predicted order of convergence is achieved even for low values of p. Moreover, in contrast to the usual h-version of the finite element method, the point at which the p-version enters the asymptotic range does not depend on problem parameters such as the Poisson ratio.
Descriptors : *Finite element analysis, *Approximation(Mathematics), Polynomials, Convergence, Ellipses, Two dimensional, Linearity, Elastic properties, Poisson ratio, Computations
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE