Non UBC
DSpace
Kovács, Balázs
2019-06-06T08:19:39Z
2018-12-07T09:06
A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the discrete surface like in Dziuk's method, 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 $H^1$-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. Numerical experiments illustrate and complement the theoretical results.
https://circle.library.ubc.ca/rest/handle/2429/70546?expand=metadata
34.0
video/mp4
Author affiliation: University of Tuebingen
Banff (Alta.)
10.14288/1.0379322
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Postdoctoral
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Numerical analysis
Partial differential equations
Scientific computing
A convergent evolving finite element algorithm for mean curvature flow of closed surfaces
Moving Image
http://hdl.handle.net/2429/70546