An Error Analysis for the Finite Element Method Applied to Convection Diffusion Problems.

Abstract

This paper analyzes the finite element method applied to a convection diffusion model problem. Linear elements are used for the trial space. The error is measured in a norm closely related to the L sup P norm. When the test space is composed of linear elements with parabolic upwinding, the method is shown to be optimal when the input data is piecewise smooth -- a condition which is usually observed in practice. Without these smoothness assumptions, the method is shown to be non-optimal, even if the class of test spaces is extended to include any elements which have a shape independent of the mesh size. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1981
Accession Number
ADA098895

Entities

People

  • Ivo Babuška
  • W. G. Szymczak

Organizations

  • University of Maryland

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Layer
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Convection
  • Diffusion
  • Equations
  • Error Analysis
  • Errors
  • Finite Element Analysis
  • Fluid Mechanics
  • Inequalities
  • Mechanics
  • Perturbation Theory
  • Physical Sciences
  • Standards

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space