On the Competition of Elastic Energy and Surface Energy in Discrete Numerical Schemes
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Submission date: 20. Dec. 2004
published in: Advances in computational mathematics, 27 (2007) 2, p. 179-194
DOI number (of the published article): 10.1007/s10444-007-9028-5
MSC-Numbers: 82C26, 74N20, 74S20
Keywords and phrases: viscosity of numerical schemes, free boundary value problems
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The -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 -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.