Convergence for mean curvature flows and anisotropy

Prof. Claudio Verdi

Dipartimento di Matematica Universita di Milano (Italy)

Motion by mean curvature arises in several applications which exhibit surface tension energies (e.g., phase transitions, crystal growth, etc.), and its numerical approximation is thus receiving considerable attention. Convergence results for discrete interfaces, including error estimates for regular and singular evolutions, are presented for a practical finite element approximation of the purely geometric problem. The anisotropic evolution is defined in the natural context of a Finsler geometry and simulations of several critical (crystalline and nonconvex) situations are shown.