Deckelnick, Klaus; Dziuk, Gerhard Convergence of a finite element method for non-parametric mean curvature flow. (English) Zbl 0838.65103 Numer. Math. 72, No. 2, 197-222 (1995). 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. Reviewer: G.Hedstrom (Livermore) Cited in 1 ReviewCited in 13 Documents MSC: 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:convergence; finite element method; mean curvature flow equation; convection-diffusion equation; Dirichlet problems; error estimates; parabolic minimal-surface equation PDFBibTeX XMLCite \textit{K. Deckelnick} and \textit{G. Dziuk}, Numer. Math. 72, No. 2, 197--222 (1995; Zbl 0838.65103) Full Text: DOI