Convergence Estimates for Semidiscrete Parabolic Equation Approximations.

Abstract

In this paper, we study certain semidiscrete methods for approximating the solutions of initial boundary value problems, with homogeneous boundary conditions, for certain kinds of parabolic equations. These semidiscrete methods are based upon the availability of several different Galerkin-type approximation methods for the associated elliptic steady-state problem. The properties required of the spacial discretization methods are listed and estimates of the error made by the resulting semidiscrete approximations and of its time derivatives are given. In particular, estimates are given that require only weak smoothness assumptions on the initial data. Verifications of the required properties for various Galerkin-type methods are also given. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1980
Accession Number
ADA086369

Entities

People

  • Peter H. Sammon

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Availability
  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Classification
  • Convergence
  • Differential Equations
  • Equations
  • Mathematics
  • New York
  • Numerical Analysis
  • Partial Differential Equations
  • Steady State
  • Two Dimensional
  • United States
  • Verification

Fields of Study

  • Mathematics

Readers

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