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Nonconforming finite-element discretization of convex variational problems
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Ortner, Christoph (2011) Nonconforming finite-element discretization of convex variational problems. IMA Journal of Numerical Analysis, Volume 31 (Number 3). pp. 847-864. doi:10.1093/imanum/drq004 ISSN 0272-4979.
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Official URL: http://dx.doi.org/10.1093/imanum/drq004
Abstract
The Lavrentiev gap phenomenon is a well-known effect in the calculus of variations, related to singularities of minimizers. In its presence, conforming finite-element methods are incapable of reaching the energy minimum. By contrast, it is shown in this work that for convex variational problems the nonconforming Crouzeix–Raviart finite-element discretization always converges to the correct minimizer and that the discrete energy converges to the correct limit.
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): | Calculus of variations, Finite element method | ||||
Journal or Publication Title: | IMA Journal of Numerical Analysis | ||||
Publisher: | Oxford University Press | ||||
ISSN: | 0272-4979 | ||||
Official Date: | July 2011 | ||||
Dates: |
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Volume: | Volume 31 | ||||
Number: | Number 3 | ||||
Page Range: | pp. 847-864 | ||||
DOI: | 10.1093/imanum/drq004 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 20 December 2015 | ||||
Date of first compliant Open Access: | 20 December 2015 | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) |
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