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. 2677-2694. ISSN 1095-7170

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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. 385--407; 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:	1095-7170
Date:	2012
Volume:	Vol.50
Number:	No.5
Page Range:	pp. 2677-2694
Identification Number:	10.1137/110828642
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/49656

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