Speaker
Description
In this talk we will present and discuss a fully discrete algorithm for mean curvature flow of closed surfaces using Lagrange multipliers for preserving the energy-decreasing structure. The algorithm is based on the solution-driven formulation using Huisken's evolution equations for the normal vector and the mean curvature. The method uses a high-order multistep methods in time and evolving surface finite elements in space.
The approach also accommodates artificial tangential velocities of minimal deformation rate-type (MDR-type). The resulting fully discrete algorithms are area-decreasing at every time step, with a prescribed decay rate determined by the computed mean curvature.
We will discuss local existence and uniqueness of the discrete Lagrange multiplier and convergence of a simplified Newton iteration for its computation under weak regularity assumptions, and present optimal-order error estimates without and with tangential motion.
The talk is based on joint work with Christian Lubich (Tübingen) and Buyang Li (PolyU Hong Kong).