The Problem of the Selection of an A-Posteriori Error Indicator Based on Smoothening Techniques

Abstract

This paper addresses the problem of assessing the quality of an a- posteriori error estimate of a finite element solution. An error estimate based on local L'-projections is analyzed in the case of translation invariant meshes. It is shown that for general meshes this technique does not lead to an asymptotically exact estimator. The problem is analyzed in detail in the one- dimensional setting. It is shown that an asymptotically exact estimator is not the optimal one when the solution is not sufficiently smooth. An optimal estimator for adaptively constructed meshes is given. Finally, a general mathematical framework for the quality assessment of estimators is introduced.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1991
Accession Number
ADA253401

Entities

People

  • Ivo M. Babuska
  • Rodolfo Rodríguez

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Coefficients
  • Computations
  • Construction
  • Differential Equations
  • Equations
  • Estimators
  • Finite Element Analysis
  • Geometry
  • Mathematical Analysis
  • Optimal Estimators
  • Partial Differential Equations
  • Periodic Functions
  • Physical Sciences
  • Polynomials
  • Theorems
  • Two Dimensional
  • Universities

Fields of Study

  • Mathematics

Readers

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