An error estimate for a new scheme for mean curvature motion

Nicolas Forcadel (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

In this work, we propose a new numerical scheme for the anisotropic mean curvature equation. The solution of the scheme is not unique, but for all numerical solutions, we provide an error estimate between the continuous solution and the numerical approximation. This error estimate is not optimal, but as far as we know, this is the first one for mean curvature type equation. Our scheme is also applicable to compute the solution to dislocations dynamics equation.

Mots clés: dislocations dynamics; Mean curvature motion; error estimate; numerical scheme; dislocations dynamics.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Nicolas Forcadel. An error estimate for a new scheme for mean curvature motion. SIAM Journal on Numerical Analysis, 2008, 46 (5), pp. 2715-2741. ⟨hal-00121795⟩