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Nonconvexity and Microstructure

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Numerical Methods for Nonlinear Partial Differential Equations

Part of the book series: Springer Series in Computational Mathematics ((SSCM,volume 47))

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Abstract

Infinite-dimensional minimization problems without convexity properties may lead to the nonexistence of solutions, but arise as simplified mathematical descriptions of crystalline phase transitions that enable the shape-memory effect of smart materials. The ill-posed minimization problems capture important effects and relaxation theories define well-posed modifications of the functionals. The problems related to direct numerical treatment of the original formulations and the convergence and numerical solution of discretizations of its modifications are investigated in this chapter.

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Authors and Affiliations

  1. Abteilung für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany

    Sören Bartels

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  1. Sören Bartels
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Bartels, S. (2015). Nonconvexity and Microstructure. In: Numerical Methods for Nonlinear Partial Differential Equations. Springer Series in Computational Mathematics, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-13797-1_9

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