Combined effect of explicit time-stepping and quadrature for curvature driven flows
The flow of a closed surface of codimension 1 in \(\mathbb{R}^n\) driven by curvature is first approximated by a singularly perturbed parabolic double obstacle problem with small parameter. The discretization is made by conforming piecewise linear finite elements, with mass lumping, over a quasi-uniform and weakly acute mesh combined with forward differences with uniform time-step. An efficient algorithm, the so-called dynamic mesh algorithm, is obtained. It shows finite speed of propagation and discrete nondegeneracy. It is demonstrated that the fully discrete solution converges past singularities to the true interface and the rate of convergence is discussed. Smooth flows are also analyzed.
scientific article; zbMATH DE number 932011