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The appearance of microstructures in problems with incompatible wells and their numerical approach

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Summary.

The goal of the paper is to analyze the creation of microstructure in problems of Calculus of Variations with wells. More precisely we consider a case with strong incompatibility between the wells. This forces the minimizing sequences to use other gradients than the wells in a puzzling way. Using a \(P_1\) method we are then able to single out discrete minimizing sequences and to give energy estimates in terms of the mesh size.

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Authors and Affiliations

  1. Angewandte Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland , , , , , , CH

    Michel Chipot

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  1. Michel Chipot
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Received December 23, 1997 / Revised version received September 7, 1998 / Published online: June 29, 1999

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Chipot, M. The appearance of microstructures in problems with incompatible wells and their numerical approach. Numer. Math. 83, 325–352 (1999). https://doi.org/10.1007/s002110050452

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  • DOI: https://doi.org/10.1007/s002110050452

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