The Optimal Convergence Rate of the p-Version of the Finite Element Method.

Abstract

The p-Version of the finite element method has been previously analyzed for elliptic problems with homogeneous boundary conditions. For a homogeneous condition of the Dirichlet type, it was shown that the exponential asymptotic convergence rate was optimal up to an arbitrarily small positive parameter epsilon. In this paper, an alternate proof is discussed which yields a better estimate by removing the dependence on epsilon. The analysis is extended to treat problems with inhomogeneous boundary conditions of both the Dirichlet and Neumann type. Estimates for a case when the solution has singularities at the corners of the domain are also provided. Keywords: Approximation(Mathematics); Polynomials.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1985
Accession Number
ADA187871

Entities

People

  • I. Babuška
  • Manil Suri

Organizations

  • University of Maryland, Baltimore County

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Boundaries
  • Boundary Value Problems
  • Convergence
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Maryland
  • Mathematics
  • Numerical Analysis
  • Periodic Functions
  • Physical Sciences
  • Polynomials
  • Scientific Research
  • Standards
  • Theorems
  • Universities

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)