A posteriori error analysis for the mean curvature flow of graphs

Lakkis, Omar and Nochetto, Ricardo H (2005) A posteriori error analysis for the mean curvature flow of graphs. SIAM Journal on Numerical Analysis, 42 (5). pp. 1875-1898. ISSN 0036-1429

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Abstract

We study the equation describing the motion of a nonparametric surface according to its mean curvature flow. This is a nonlinear nonuniformly parabolic PDE that can be discretized in space via a finite element method. We conduct an aposteriori error analysis of the spatial discretization and derive upper bounds on the error in terms of computable estimators based on local residual indicators. The reliability of the estimators is illustrated with two numerical simulations, one of which treats the case of a singular solution.

Item Type: Article
Additional Information: Copyright owned by SIAM Journal on Numerical Analysis. Appropriate permissions should be sought before making any use of this article for purposes other than private research.
Keywords: finite element; efficiency; sharp estimates; effectivity index; mean curvature; error analysis; a posteriori; nonlinear PDE; parabolic equation; geometric motion; convergence; reliability
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA0076 Computer software
Depositing User: Omar Lakkis
Date Deposited: 27 Jul 2007
Last Modified: 07 Mar 2017 06:35
URI: http://sro.sussex.ac.uk/id/eprint/1227
Google Scholar:11 Citations

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