A General Finite Difference Method for Arbitrary Meshes,

Abstract

A two-dimensional finite difference technique for irregular meshes is suggested to obtain derivatives up to the order of two. The technique enjoys two major advantages: (1) avoidance of singularity in derivative coefficient matrix, and (2) better accuracy of derivatives than that obtained previously. For square meshes general derivative expressions for arbitrary meshes reduce to the usual central finite difference formulae. Example problems solved are a Poisson equation and the large deflection of a square flat membrane; the solutions compare quite well with results obtained elsewhere. For problems with higher order derivative terms, two possible approaches are discussed. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1972
Accession Number
AD0738982

Entities

People

  • Nicholas Perrone
  • Robert Kao

Organizations

  • The Catholic University of America

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Coefficients
  • Deflection
  • Differential Equations
  • Equations
  • Mathematics
  • Membranes
  • Partial Differential Equations
  • Poisson Equation
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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