Mixed explicit‐implicit iterative finite element scheme for diffusion‐type problems: I. Theory

S. P. Neuman, T. N. Narasimhan

Research output: Contribution to journalArticle

30 Scopus citations

Abstract

A Galerkin finite element formulation of diffusion processes based on a diagonal capacity matrix is analysed from the standpoint of local stability and convergence. The theoretical analysis assumes that the conductance matrix is locally diagonally dominant, and it is shown that one can always construct a finite element network of linear triangles satisfying this condition. Time derivatives are replaced by finite differences, leading to a mixed explicit‐implicit system of algebraic equations which can be efficiently solved by a point iterative technique. In this work the accelerated point iterative method is adopted and is shown to converge when the conductance matrix is locally diagonally dominant. Several examples are included in Part II of this paper to demonstrate the efficiency of the new approach.

Original languageEnglish (US)
Pages (from-to)309-323
Number of pages15
JournalInternational Journal for Numerical Methods in Engineering
Volume11
Issue number2
DOIs
StatePublished - 1977

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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