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A fully discrete evolving surface finite element method
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Dziuk, Gerhard and Elliott, Charles M.. (2012) A fully discrete evolving surface finite element method. SIAM Journal of Numerical Analysis, Vol.50 (No.5). pp. 26772694. ISSN 10957170

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Official URL: http://www.siam.org/journals/sinum.php
Abstract
In this paper we consider a time discrete evolving surface finite element method for the advection and diffusion of a conserved scalar quantity on a moving surface. In earlier papers using a suitable variational formulation in time dependent Sobolev space we proposed and analyzed a finite element method using surface finite elements on evolving triangulated surfaces [IMA J. Numer Anal., 25 (2007), pp. 385407; Math. Comp., to appear]. Optimal order L2(Γ(t)) and H1(Γ(t)) error bounds were proved for linear finite elements. In this work we prove optimal order error bounds for a backward Euler time discretization.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Mathematics 
Library of Congress Subject Headings (LCSH):  Finite element method 
Journal or Publication Title:  SIAM Journal of Numerical Analysis 
Publisher:  Society for Industrial and Applied Mathematics 
ISSN:  10957170 
Official Date:  2012 
Volume:  Vol.50 
Number:  No.5 
Page Range:  pp. 26772694 
Identification Number:  10.1137/110828642 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
References:  [1] D. Adalsteinsson and J. A. Sethian, Transport and diffusion of material quantities on 
URI:  http://wrap.warwick.ac.uk/id/eprint/49656 
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