An Optimum Formulation of the Finite Element Method for the Diffusion Equation.

Abstract

In an earlier paper, the Crandall and Crank-Nicolson (CNM) finite difference methods were compared with respect to the solution of the transient heat conduction problem (isomorphic with respect to the diffusion equation). In this paper, an optimum formulation of the finite element method for the diffusion equation is derived. This method is the finite element equivalent of the Crandall method for finite differences. The method is then applied to problems with Neumann and Dirichlet boundary conditions, and the accuracy is compared with the finite element version of the CNM.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1987
Accession Number
ADA182494

Entities

People

  • Charles R. Martin

Organizations

  • Air Command and Staff College

Tags

Communities of Interest

  • Counter WMD
  • Weapons Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Boundaries
  • Difference Equations
  • Differential Equations
  • Eigenvalues
  • Engineering
  • Equations
  • Finite Element Analysis
  • Heat Transfer
  • North Carolina
  • Nuclear Engineering
  • Partial Differential Equations
  • Training
  • Truncation
  • United States
  • Universities

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)