
Accession Number : ADA140952
Title : The Approximation Theory for the PVersion 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 pversion 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 nonsmooth parts of the domain boundaries. Numerical results for two problems from twodimensional 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 hversion of the finite element method, the point at which the pversion 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