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Minimum time-step size for diffusion problem in FEM analysis

✍ Scribed by H. R. Thomas; Z. Zhou

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 134 KB
Volume: 40
Category: Article
ISSN: 0029-5981
DOI: 10.1002/(sici)1097-0207(19971030)40:20<3865::aid-nme246>3.0.co;2-c

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✦ Synopsis

In this paper oscillation of results arising from the use of a time-step size which is less than the minimum required is examined. The phenomenon is summarised to give two requirements that the solution of boundary problems has to satisfy. An approach to derive the minimum time-step size for various kinds of elements is developed. A theoretical verification is presented for the one-dimensional two-noded element case and a numerical examination of the criteria explored for the two-dimensional eight-noded element case.

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The solution of the equation system of the ®nite element method for diusion problems is presented in the format of a sequence. The characteristics of the numerical results can thus be known through an analysis of this `theoretical expression' of the solution. The characteristics of the sequence are