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The Numerical Computation of Singular Minimizers in Two-Dimensional Elasticity

✍ Scribed by Pablo V. Negrón-Marrero; Octavio Betancourt

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
554 KB
Volume
113
Category
Article
ISSN
0021-9991

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✦ Synopsis

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, the.

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✍ F. Assous; P. Ciarlet Jr.; J. Segré 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 472 KB

In this paper, we present a method to solve numerically the time-dependent Maxwell equations in nonsmooth and nonconvex domains. Indeed, the solution is not of regularity H 1 (in space) in general. Moreover, the space of H 1 -regular fields is not dense in the space of solutions. Thus an H 1 -confor