An Analysis of a Finite Element Method for Convection-Diffusion Problems. Part I. Quasi-Optimality.

Abstract

A detailed analysis is performed for a finite element method applied to the general one-dimensional convection diffusion problem. Piecewise polynomials are used for the trial space. The test space is formed by locally projecting L-spline basis functions onto upwinded polynomials. The error is measured in the LP mesh dependent norm. The method is proven to be quasi-optimal (yielding nearly the best approximation from the trial space), provided that the input data is piecewise smooth. This assumption is usually observed in practice. These results are used to establish a posteriori error estimates and an adaptive mesh refinement strategy in Part II of this series (35). (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1983
Accession Number
ADA128260

Entities

People

  • Ivo Babuška
  • W. G. Szymczak

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Weapons Technologies

DTIC Thesaurus Topics

  • Asymptotic Series
  • Boundary Layer
  • Boundary Value Problems
  • Contracts
  • Convection
  • Diffusion
  • Equations
  • Finite Element Analysis
  • Inequalities
  • Maryland
  • Military Research
  • Numerical Analysis
  • Physical Sciences
  • Standards
  • Theorems
  • Two Dimensional
  • Universities

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space