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.