An Analysis of a Finite Element Method for Convection-Diffusion Problems. Part II. A Posteriori Error Estimates and Adaptivity.

Abstract

A posteriori error estimates are derived for the finite element method presented in Part I. These estimates are proven to have the property that the effectivity index theta = (error estimate/true error) converges to one as the maximum mesh size goes to zero. An adaptive mesh refinement strategy is based on equilibriating local error indicators whose sum comprises the global error estimate. Numerical results show that theta is nearly one even on coarse meshes, and that optimal meshes are created by the adaptive procedure. The successful solution of a non linear problem-modelling flow through an expanding duct, makes evident the robustness of the method. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1983
Accession Number
ADA128261

Entities

People

  • Ivo Babuška
  • W. G. Szymczak

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I
  • Weapons Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Applied Mathematics
  • Boundary Layer
  • Computations
  • Convection
  • Diffusion
  • Equations
  • Estimators
  • Finite Element Analysis
  • Layers
  • Maryland
  • Military Research
  • Models
  • Numerical Analysis
  • Physical Sciences
  • Two Dimensional

Readers

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