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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. 346367. ISSN 00361429

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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  

Subjects:  Q Science > QA Mathematics  
Divisions:  Faculty of 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:  00361429  
Official Date:  22 February 2011  
Dates: 


Volume:  Volume 49  
Number:  Number 1  
Page Range:  pp. 346367  
Identification Number:  10.1137/090781073  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
Funder:  Engineering and Physical Sciences Research Council (EPSRC)  
Adapted As:  
References:  [1] G. Acosta and R. G. Dur´ an, An optimal Poincar´e inequality in L1 for convex domains, Proc. 

URI:  http://wrap.warwick.ac.uk/id/eprint/43788 
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