Error analysis of a finite element scheme for parametric mean curvature flow based on the DeTurck trick
Provides rigorous error analysis for a numerical method for geometric flows, benefiting computational geometry and PDE communities.
The paper proves an optimal H^1-error estimate for a finite element scheme for parametric mean curvature flow using the DeTurck trick, with numerical experiments confirming the bound.
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 using the DeTurck trick and was proposed by Elliott and Fritz in [15]. In the semidiscrete case, for a spatial discretization by finite elements of order $k \geq 2$ we prove an optimal $H^1$-error estimate for the position vector. We present numerical experiments that confirm this error bound and demonstrate that the scheme has good properties with respect to the distribution of mesh points as already observed in [15].