Stability of flat interfaces during semidiscrete solidification
Dipartimento di Matematica, Università degli Studi di Milano,
Via C. Saldini 50, 20133 Milano, Italy. email@example.com.
(On leave from) Institut für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 10, 79104 Freiburg, Germany. firstname.lastname@example.org.
Revised: 4 March 2002
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.
Mathematics Subject Classification: 65M12 / 65M60
Key words: (Mullins-Sekerka) stability analysis / morphological instabilities / spatial semidiscretization / moving finite elements / phase transitions / surface tension / Stefan condition / dendritic growth / secondary sidebranching.
© EDP Sciences, SMAI, 2002