Analysis of Evolutionary Error in Finite Element and Other Methods.

Abstract

Restriction and prolongation operators are used to provide a unified framework for the discussion of errors in approximating evolutionary equations. A generalized truncation error enables the spline-Galerkin method to be studied in detail and the accuracy of various treatments of non-linear terms (such as the advection operator v dot del(v) compared: it is shown how a multi-stage Galerkin process can give errors which are 0(h to the 2mu power) for splines of order mu and quite general differential operators. A Petrov-Galerkin method is derived for partial sub t = a(partial sub x of u) which is accurate and stable. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1978
Accession Number
ADA054551

Entities

People

  • K. W. Morton
  • M. J. P. Cullen

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Computational Fluid Dynamics
  • Computational Science
  • Difference Equations
  • Differential Equations
  • Equations
  • Errors
  • Finite Element Analysis
  • Fluid Dynamics
  • Fluid Flow
  • Formulas (Mathematics)
  • Fourier Analysis
  • Galerkin Method
  • Mathematics
  • Mechanical Properties
  • Numerical Analysis
  • Partial Differential Equations
  • United States

Fields of Study

  • Mathematics

Readers

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