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A finite element error analysis for axisymmetric mean curvature flow

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1911.05398v1.pdfWorking paper875.83 kBAdobe PDFView/Open
Title: A finite element error analysis for axisymmetric mean curvature flow
Authors: Barrett, JW
Deckelnick, K
Nürnberg, R
Item Type: Working Paper
Abstract: We consider the numerical approximation of axisymmetric mean curvature flow with the help of linear finite elements. In the case of a closed genus-1 surface, we derive optimal error bounds with respect to the $L^2$-- and $H^1$--norms for a fully discrete approximation. We perform convergence experiments to confirm the theoretical results, and also present numerical simulations for some genus-0 and genus-1 surfaces.
Issue Date: 13-Nov-2019
URI: http://hdl.handle.net/10044/1/75880
Publisher: arXiv
Copyright Statement: © 2019 The Author(s)
Keywords: math.NA
math.NA
cs.NA
65M60, 65M12, 65M15, 53C44, 35K55
math.NA
math.NA
cs.NA
65M60, 65M12, 65M15, 53C44, 35K55
Notes: 20 pages, 7 figures
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics