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L² -estimates for the evolving surface finite element method
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Dziuk, Gerhard and Elliott, Charles M. (2012) L² -estimates for the evolving surface finite element method. Mathematics of Computation, Volume 82 (Number 281). pp. 1-24. doi:10.1090/S0025-5718-2012-02601-9 ISSN 0025-5718.
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Official URL: http://dx.doi.org/10.1090/S0025-5718-2012-02601-9
Abstract
In this paper we consider the evolving surface finite element method
for the advection and diffusion of a conserved scalar quantity on a moving
surface. In an earlier paper using a suitable variational formulation in time
dependent Sobolev space we proposed and analysed a finite element method
using surface finite elements on evolving triangulated surfaces. An optimal
order H¹ -error bound was proved for linear finite elements. In this work we
prove the optimal error bound in L² (Γ(t)) uniformly in time.
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 analysis, Numerical analysis, Mathematical analysis | ||||
Journal or Publication Title: | Mathematics of Computation | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 0025-5718 | ||||
Official Date: | April 2012 | ||||
Dates: |
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Volume: | Volume 82 | ||||
Number: | Number 281 | ||||
Page Range: | pp. 1-24 | ||||
DOI: | 10.1090/S0025-5718-2012-02601-9 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 24 December 2015 | ||||
Date of first compliant Open Access: | 24 December 2015 | ||||
Funder: | Deutsche Forschungsgemeinschaft (DFG), Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | SFB/TR 71 (DFG), EP/G010404 (EPSRC) |
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