Mixed explicit‐implicit iterative finite element scheme for diffusion‐type problems: II. Solution strategy and examples

T. N. Narasimhan, Shlomo P Neuman, A. L. Edwards

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In Part I1 of this paper we have established local stability and convergence criteria for the mixed explicit‐implicit finite element scheme and have shown that the proposed iterative method converges under certain conditions. Part II describes various practical aspects of the solution strategy such as convergence criteria for terminating the iterations, automatic control of time step size, reclassification of nodes from explicit to implicit during execution, estimation of time derivatives, and automatic adjustment of the implicit weight factor. Several examples are included to demonstrate certain aspects of the theory and illustrate the capabilities of the new approach.

Original languageEnglish (US)
Pages (from-to)325-344
Number of pages20
JournalInternational Journal for Numerical Methods in Engineering
Volume11
Issue number2
DOIs
StatePublished - 1977

Fingerprint

Convergence Criteria
Iterative methods
Finite Element
Derivatives
Iteration
A.s. Convergence
Automatic Control
Mixed Finite Elements
Local Convergence
Local Stability
Stability and Convergence
Stability Criteria
Adjustment
Converge
Derivative
Vertex of a graph
Demonstrate
Strategy

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

Cite this

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AU - Neuman, Shlomo P

AU - Edwards, A. L.

PY - 1977

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AB - In Part I1 of this paper we have established local stability and convergence criteria for the mixed explicit‐implicit finite element scheme and have shown that the proposed iterative method converges under certain conditions. Part II describes various practical aspects of the solution strategy such as convergence criteria for terminating the iterations, automatic control of time step size, reclassification of nodes from explicit to implicit during execution, estimation of time derivatives, and automatic adjustment of the implicit weight factor. Several examples are included to demonstrate certain aspects of the theory and illustrate the capabilities of the new approach.

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