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On the convergence of adaptive nonconforming finite element methods for a class of convex variational problems
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Ortner, Christoph and Praetorius, Dirk (2011) On the convergence of adaptive nonconforming finite element methods for a class of convex variational problems. SIAM Journal on Numerical Analysis, Volume 49 (Number 1). pp. 346-367. doi:10.1137/090781073 ISSN 0036-1429.
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Official URL: http://dx.doi.org/10.1137/090781073
Abstract
We formulate and analyze an adaptive nonconforming finite element method for the solution of convex variational problems. The class of minimization problems we admit includes highly singular problems for which no Euler–Lagrange equation (or inequality) is available. As a consequence, our arguments only use the structure of the energy functional. We are nevertheless able to prove convergence of an adaptive algorithm, using even refinement indicators that are not reliable error indicators.
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, Calculus of variations | ||||||||
Journal or Publication Title: | SIAM Journal on Numerical Analysis | ||||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||||
ISSN: | 0036-1429 | ||||||||
Official Date: | 22 February 2011 | ||||||||
Dates: |
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Volume: | Volume 49 | ||||||||
Number: | Number 1 | ||||||||
Page Range: | pp. 346-367 | ||||||||
DOI: | 10.1137/090781073 | ||||||||
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) | ||||||||
Adapted As: |
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