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Error control and adaptivity for a variational model problem defined on functions of bounded variation


Author: Sören Bartels
Journal: Math. Comp. 84 (2015), 1217-1240
MSC (2010): Primary 65N30, 65N50
DOI: https://doi.org/10.1090/S0025-5718-2014-02893-7
Published electronically: October 23, 2014
MathSciNet review: 3315506
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Abstract: We derive a fully computable, optimal a posteriori error estimate for the finite element approximation of a total variation regularized model problem and devise an adaptive refinement strategy. Numerical experiments reveal a significant improvement over related approximations on uniformly refined triangulations.


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Additional Information

Sören Bartels
Affiliation: Abteilung für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg, Hermann-Herder Str. 10, 79104 Freiburg i.Br., Germany
Email: bartels@mathematik.uni-freiburg.de

DOI: https://doi.org/10.1090/S0025-5718-2014-02893-7
Keywords: Total variation, functions of bounded variation, finite elements, adaptivity, error estimation
Received by editor(s): July 17, 2012
Received by editor(s) in revised form: March 11, 2013, July 24, 2013, and September 17, 2013
Published electronically: October 23, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.