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Zbl 1137.65404
Veeser, Andreas
Stability of flat interfaces during semidiscrete solidification. (English)
[J] M2AN, Math. Model. Numer. Anal. 36, No. 4, 573-595 (2002). ISSN 0764-583X; ISSN 1290-3841/e

Summary: The stability of flat interfaces with respect to a spatial semidiscretization of a solidification model is analyzed. The considered model is the quasi-static approximation of the Stefan problem with dynamical Gibbs-Thomson law. The stability analysis bases on an argument developed by Mullins and Sekerka for the undiscretized case. The obtained stability properties differ from those with respect to the quasi-static model for certain parameter values and relatively coarse meshes. Moreover, consequences on discretization issues are discussed.

MSC 2000:: *65M12 Stability and convergence of numerical methods (IVP of PDE)
65M60 Finite numerical methods (IVP of PDE)

Keywords: Mullins-Sekerka stability analysis; morphological instabilities; spatial semidiscretization; moving finite elements; phase transitions; surface tension; Stefan condition; dendritic growth; secondary sidebranching

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