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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...
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,...
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