Analysis of a Subdomain-Based Error Estimator for Finite Element Approximations of Elliptic Problems

Abstract

In this paper we analyze a sub-domain residual error estimator for finite element approximations of elliptic problems. It is obtained by solving local problems on patches of elements in weighted spaces and provides for an upper bound on the energy norm of the error when the local problems are solved in sufficiently enriched discrete spaces. a guaranteed lower bound on the error is also derived by a simple post process of the solutions to the local problems. Numerical tests show very good effectivity indices for both the upper and lower bounds and a strong reliability of this estimator even for coarse meshes.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2005
Accession Number
ADA438141

Entities

People

  • F. Nobile
  • J. T. Oden
  • L. Chamoin
  • S. Prudhomme

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Applied Mathematics
  • Boundaries
  • Boundary Value Problems
  • Errors
  • Estimators
  • Inequalities
  • Mathematics
  • Orthogonality
  • Polynomials
  • Residuals
  • Statistical Algorithms
  • Three Dimensional
  • Triangles
  • Two Dimensional
  • Weighting Functions

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Statistical inference.

Technology Areas

  • Space