Nochetto, Ricardo H.; Verdi, Claudio Combined effect of explicit time-stepping and quadrature for curvature driven flows. (English) Zbl 0859.65066 Numer. Math. 74, No. 1, 105-136 (1996). 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. Reviewer: V.Arnăutu (Iaşi) Cited in 1 ReviewCited in 10 Documents MSC: 65K10 Numerical optimization and variational techniques 35K57 Reaction-diffusion equations 35B25 Singular perturbations in context of PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 49Q05 Minimal surfaces and optimization 49M15 Newton-type methods 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 35B50 Maximum principles in context of PDEs 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature Keywords:explicit time-stepping; quadrature; curvature driven flows; double obstacle problem; linear finite elements; dynamic mesh algorithm; convergence PDFBibTeX XMLCite \textit{R. H. Nochetto} and \textit{C. Verdi}, Numer. Math. 74, No. 1, 105--136 (1996; Zbl 0859.65066) Full Text: DOI