Singularities in p-Type Finite Element Computations: Numerical Experiments on the Locality of Pollution Effects

[+] Author and Article Information
G. Becker, P. Carnevali, B. Chayapathy, W. Imaino, R. B. Morris, Y. Tsuji, B. Yendler

IBM Research Division, Almaden Research Center, San Jose, CA 95120-6099

J. Appl. Mech 58(2), 586-588 (Jun 01, 1991) (3 pages) doi:10.1115/1.2897228 History: Received November 17, 1989; Revised April 15, 1990; Online March 31, 2008


Using a recently developed code for three-dimensional p -type finite element computations in elasticity, we have studied, with a series of numerical experiments, the behavior of the solution in the presence of singularities. Worst-cast theoretical estimates predict a global pollution of the solution, unless optimally graded meshes are used. On the other hand, we observe that except in an immediate neighborhood of a singularity, and even using uniform meshes, the quality of the solution is not degraded to any practically relevant extent. This has important practical consequences because it allows modelers to introduce artifical singularities for the purpose of simplifying models. The size of the area around a singularity where the solution is appreciably degraded can be estimated in terms of the minimum effective wavelength of the basis functions used; the latter, in turn, can be related to the element size and the polynomial order used.

Copyright © 1991 by The American Society of Mechanical Engineers
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