IRUS Total

Stable approximations for axisymmetric Willmore flow for closed and open surfaces

File Description SizeFormat 
1911.01132v1.pdfWorking paper1.69 MBAdobe PDFView/Open
Title: Stable approximations for axisymmetric Willmore flow for closed and open surfaces
Authors: Barrett, JW
Garcke, H
Nürnberg, R
Item Type: Working Paper
Abstract: For a hypersurface in ${\mathbb R}^3$, Willmore flow is defined as the $L^2$--gradient flow of the classical Willmore energy: the integral of the squared mean curvature. This geometric evolution law is of interest in differential geometry, image reconstruction and mathematical biology. In this paper, we propose novel numerical approximations for the Willmore flow of axisymmetric hypersurfaces. For the semidiscrete continuous-in-time variants we prove a stability result. We consider both closed surfaces, and surfaces with a boundary. In the latter case, we carefully derive suitable boundary conditions. Furthermore, we consider many generalizations of the classical Willmore energy, particularly those that play a role in the study of biomembranes. In the generalized models we include spontaneous curvature and area difference elasticity (ADE) effects, Gaussian curvature and line energy contributions. Several numerical experiments demonstrate the efficiency and robustness of our developed numerical methods.
Issue Date: 4-Nov-2019
URI: http://hdl.handle.net/10044/1/75884
Publisher: arXiv
Copyright Statement: © 2019 The Author(s)
Keywords: math.NA
65M60, 65M12, 35K55, 53C44
65M60, 65M12, 35K55, 53C44
Notes: 66 pages, 13 figures
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics