Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/92476
Title: | A convergent evolving finite element algorithm for mean curvature flow of closed surfaces | Authors: | Kovács, B Li, B Lubich, C |
Issue Date: | Dec-2019 | Source: | Numerische mathematik, Dec. 2019, v. 143, no. 4, p. 797-853 | Abstract: | 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 in the case of finite elements of polynomial degree at least two and backward difference formulae of orders two to five. The error analysis combines stability estimates and consistency estimates to yield optimal-order H1-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. | Publisher: | Springer | Journal: | Numerische mathematik | ISSN: | 0029-599X | EISSN: | 0945-3245 | DOI: | 10.1007/s00211-019-01074-2 | Rights: | © Springer-Verlag GmbH Germany, part of Springer Nature 2019 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00211-019-01074-2 |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Kovacs_Convergent_Evolving_Finite.pdf | Pre-Published version | 3.87 MB | Adobe PDF | View/Open |
Page views
53
Last Week
1
1
Last month
Citations as of May 5, 2024
Downloads
76
Citations as of May 5, 2024
SCOPUSTM
Citations
38
Citations as of Apr 26, 2024
WEB OF SCIENCETM
Citations
37
Citations as of May 2, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.