Convergence of a finite element method for non-parametric mean curvature flow
This paper is devoted to a finite element method for the mean curvature flow equation, a convection-diffusion equation in which the convection depends on the mean curvature of the level surfaces. Dirichlet problems are considered on a bounded domain \(\Omega\) in the plane. For the finite element method \(\Omega\) is divided into triangles, for which a side on \(\partial \Omega\) may be curved. The basis functions are linear on each triangle. Convergence proofs and error estimates are given. The proofs are based on a homotopy from the parabolic minimal-surface equation.
scientific article; zbMATH DE number 839155