Dispersion Analysis and Error Estimation of Galerkin Finite Element Methods for the Numerical Computation of Waves

Abstract

The authors' recent result on the phase difference for one-dimensional problems in numerically evaluated and discussed in the context of other work directed to this topic. It is shown that previous error estimates in integral norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only. On the other hand, recently proven error estimates on normalized mesh contain a pollution term. With certain assumptions on the exact solution, this term is of the order of the phase difference. Thus a link is established between the results of dispersion analysis and the results of numerical analysis. (AN)

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Document Details

Document Type
Technical Report
Publication Date
Jul 26, 1994
Accession Number
ADA290296

Entities

People

  • Frank Ihlenburg
  • Ivo Babuška

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Computational Science
  • Computations
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Frequency
  • Galerkin Method
  • Helmholtz Equations
  • Mathematics
  • Numerical Analysis
  • Partial Differential Equations
  • Physical Sciences
  • Test And Evaluation
  • Theorems
  • Two Dimensional
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Theoretical Analysis.
  • Wave Propagation and Nonlinear Chaotic Dynamics.