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Convergence of a finite element method for non-parametric mean curvature flow. (English) Zbl 0838.65103
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.

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
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