Ritz-Galerkin Methods for Singular Boundary Value Problems.

Abstract

This paper is concerned with the application of the Ritz-Galerkin method to the numerical solution of singular boundary value problems of the type arising when Poisson's equation on a domain with cylindrical or spherical symmetry is reduced to a one-dimensional problem. The objective is to derive a priori estimates for the error. The difficulty is that these norms are not natural norms for the reduced problem. With the aid of B-splines we prove some nonstandard approximation - theoretic results and use these to derive the desired error estimates. Some numerical results are presented.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1977
Accession Number
ADA042735

Entities

People

  • Dennis Jespersen

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Complex Variables
  • Contracts
  • Convergence
  • Differential Equations
  • Equations
  • Galerkin Method
  • Gaussian Quadrature
  • Mathematics
  • North Carolina
  • Numerical Analysis
  • Polynomials
  • Symmetry
  • Theorems
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

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