Finite Element Methods for Spherically Symmetric Elliptic Equations.

Abstract

This paper considers the numerical solution of elliptic partial differential equations in spherical domains. When all the functions involved are spherically symmetric (that is, they depend only on distance from the center of the domain), the problem can be replaced by an equivalent two-point boundary value problem. The resulting problem is singular, but nevertheless has a smooth solution. It should therefore be possible to approximate the solution accurately using the Rayleigh-Ritz Galerkin method with a piecewise polynomial subspace on a quasiuniform mesh. Optimal-order error bounds will be obtained, showing that this procedure is theoretically well-founded. Instead of the usual Sobolev norms, norms are used which are appropriate to the original n-dimensional setting of the problem.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 01, 1977
Accession Number
ADA047721

Entities

People

  • Martin H. Schultz
  • R. S. Schreiber
  • S. C. Eisenstat

Organizations

  • Yale University

Tags

DTIC Thesaurus Topics

  • Bits
  • Boundaries
  • Boundary Value Problems
  • Computer Science
  • Computers
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Galerkin Method
  • Gaussian Quadrature
  • Intervals
  • Numerical Analysis
  • Numerical Quadrature
  • Partial Differential Equations
  • Polynomials
  • Symmetry
  • Theorems

Fields of Study

  • Mathematics

Readers

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