3 papers
math.NA2026
Error analysis of a finite element scheme for parametric mean curvature flow based on the DeTurck trick
Klaus Deckelnick, Vanessa Styles
The paper is concerned with the error analysis of a numerical scheme for the approximation of parametric mean curvature flow. The scheme we study is based on a reparametrization us…
math.OC2026
Global convergence of -steepest descent for PDE constrained shape optimisation with semilinear elliptic equations in function space
Klaus Deckelnick, Philip J. Herbert, Michael Hinze
We prove global convergence in function space for the steepest descent method in shape optimisation with semilinear elliptic partial differential equations. Steepest descent is rea…
math.NA2025
Error estimates for a surface finite element method for anisotropic mean curvature flow
Klaus Deckelnick, Harald Garcke, Balázs Kovács
Error estimates are proved for an evolving surface finite element semi-discretization for anisotropic mean curvature flow of closed surfaces. For the geometric surface flow, a syst…