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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. 2677-2694. doi:10.1137/110828642 ISSN 1095-7170.
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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. 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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Vol.50 | ||||
Number: | No.5 | ||||
Page Range: | pp. 2677-2694 | ||||
DOI: | 10.1137/110828642 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 22 December 2015 | ||||
Date of first compliant Open Access: | 22 December 2015 |
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