A finite element method for surface diffusion: the parametric case.
type: Item
instance of: scholarly article
title: A finite element method for surface diffusion: the parametric case.
zbMATH Open document ID: 1070.65093
author: Eberhard Bänsch
author: Ricardo H. Nochetto
author: Pedro Morin
published in: Journal of Computational Physics
publication date: 2005-02-09T00:00:00Z
full work available at URL: http://cimec.org.ar/ojs/index.php/cmm/article/view/230
review text: Surface diffusion is a geometry driven motion of a surface with normal velocity proportional to the surface Laplacian of mean curvature. It is described by a system of two second order nonlinear equations involving the Laplace-Beltrami operator. The system is discretized semi-implicitly in time. A system of linear elliptic partial differential equations needs to be solved at every time step. The spatial discretization uses continuous, piecewise polynomial finite elements. The solution of the resulting linear algebraic system is described in detail. The authors present possible obstacles when implementing the algorithm and show ways how to overcome them (mesh regularization, time-step control, mesh adaptation etc.). The exposition of the algorithm, supported by useful examples of computations, is clear, the results are convincing.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M50
zbMATH DE Number: 2132615
zbMATH Keywords: surface diffusion
zbMATH Keywords: fourth-order parabolic problem
zbMATH Keywords: finitel elements
zbMATH Keywords: Schur decomposition
zbMATH Keywords: smoothing effect
zbMATH Keywords: pinch-off
zbMATH Keywords: numerical examples
zbMATH Keywords: algorithm
zbMATH Keywords: mesh regularization
zbMATH Keywords: time-step control
zbMATH Keywords: mesh adaptation
reviewed by: Jiří Horák
describes a project that uses: ALBERT
MaRDI profile type: Publication
OpenAlex ID: W2061871850
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DOI: 10.1016/J.JCP.2004.08.022
description: scientific article; zbMATH DE number 2132615