Fourier Analysis of Finite Element Preconditioned Collocation Schemes

Abstract

This paper investigates the spectrum of the iteration operator of soman finite element preconditioned Fourier collocation schemes. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the transverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1990
Accession Number
ADA227363

Entities

People

  • Ernest H. Mund
  • Michel O. Deville

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Advection
  • Differential Equations
  • Diffusion
  • Eigenvalues
  • Eigenvectors
  • Engineering
  • Equations
  • Fluid Flow
  • Fourier Analysis
  • Iterations
  • Navier Stokes Equations
  • Numerical Analysis
  • Reynolds Number
  • Spectra
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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