Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Dr. Balazs Kovacs, University of Tuebingen
Inviter:
Title:
A convergent algorithm for mean curvature flow
Time & Venue:
2019.09.13 09:00-09:45 N204
Abstract:
We will sketch a proof of convergence is for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The proposed and studied numerical method combines evolving surface finite elements, whose nodes determine the discrete surface like in Dziuk's algorithm proposed in 1990, and linearly implicit backward difference formulae for time integration. The proposed method differs from Dziuk's approach in that it discretizes Huisken's evolution equations for the normal vector and mean curvature and uses these evolving geometric quantities in the velocity law projected to the finite element space. This numerical method admits a convergence analysis, which combines stability estimates and consistency estimates to yield optimal-order -norm error bounds for the computed surface position, velocity, normal vector and mean curvature. The stability analysis is based on the matrix-vector formulation of the finite element method and does not use geometric arguments. The geometry enters only into the consistency estimates. We will also present various numerical experiments to illustrate and complement the theoretical results. Furthermore, we will give an outlook towards problems coupling mean curvature forced by a surface PDE.
Appendix：
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