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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
94/2004

On the Competition of Elastic Energy and Surface Energy in Discrete Numerical Schemes

Thomas Blesgen

Abstract

The $\Gamma$-limit of certain discrete free energy functionals related to the numerical approximation of Ginzburg-Landau models is analysed when the distance $h$ between neighbouring points tends to zero. The main focus lies on cases where there is competition between surface energy and elastic energy. Two discrete approximation schemes are compared, one of them shows a surface energy in the $\Gamma$-limit. Finally, numerical solutions for the sharp interface Cahn-Hilliard model with linear elasticity are investigated. It is demonstrated how the viscosity of the numerical scheme introduces an artifical surface energy that leads to unphysical solutions.

Received:
Dec 20, 2004
Published:
Dec 20, 2004
MSC Codes:
82C26, 74N20, 74S20
Keywords:
viscosity of numerical schemes, free boundary value problems

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inJournal
2007 Repository Open Access
Thomas Blesgen

On the competition of elastic energy and surface energy in discrete numerical schemes

In: Advances in computational mathematics, 27 (2007) 2, pp. 179-194