98-12   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Andreas Prohl:

An adaptive Finite Element method for solving a double well problem describing crystalline microstructure

The minimization of nonconvex functionals naturally arises in material sciences where deformations of certain alloys exhibit microstructures. As an example, minimizing sequences of the nonconvex Ericksen-James energy can be associated to deformations in martensitic materials that are observed in experiments. - From the numerical point of view, classical conforming and nonconforming finite element discretizations have been observed to give minimizers with their quality being highly mesh dependent. In order to make the quality of the computed minimizer more independent from the applied triangulation, a new approach based on discontinuous finite elements has been proposed and analyzed recently. The present paper is devoted to propose and analyze an adaptive method - using discontinuous finite elements - to resolve microstructures on arbitrary grids, in order to obtain a more accurate resolution of laminate microstructure.

Keywords: Adaptive algorithm, finite element method, non-convex minimization, multi-well problem, microstructure, multiscale, nonlinear elasticity, shape-memory alloy, materials science

Mail an Jens Burmeister
[Thu Feb 19 18:56:34 2009]
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