The Approximation Theory for the P-Version of the Finite Element Method. II.

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.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1984
Accession Number
ADA140952

Entities

People

  • M. R. Dorr

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Mechanics
  • Computational Science
  • Coordinate Systems
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Mathematics
  • Mechanics
  • New York
  • Numerical Analysis
  • Partial Differential Equations
  • Poisson Ratio
  • Real Numbers
  • Theorems
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Graph Algorithms and Convex Optimization.