THE NUMERICAL COMPUTATION OF SINGULAR MINIMIZERS IN 2-DIMENSIONAL ELASTICITY

In this paper we use a spectral-collocation method for the computation of singular minimizers in two-dimensional elasticity. In particular we are interested in computing cavitating solutions (those that open a hole at the center) and determining whether or not they are globally stable in the energy sense. We describe the spectral collocation method which is used in conjunction with a Richardson extrapolation iteration and discuss various aspects related to the convergence of the method. We obtain a variety of results for certain ranges of parameters that show how the size of the cavitation depends on these parameters. (C) 1994 Academic Press, Inc.