Volume 56, Number 6, November-December 2022
|Page(s)||1871 - 1888|
|Published online||12 August 2022|
Singular solutions, graded meshes,and adaptivity for total-variation regularized minimization problems
Abteilung für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 10, 79104 Freiburg i. Br., Germany
2 INRIA de Paris, 2 Rue Simone IFF, 75012 Paris, France
* Corresponding author: firstname.lastname@example.org
Accepted: 23 June 2022
Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and devise numerical methods using locally refined meshes that lead to improved convergence rates despite the occurrence of discontinuities. It turns out that linear convergence is possible on suitably constructed meshes.
Mathematics Subject Classification: 49M29 / 65N15 / 65N50
Key words: Nonsmooth minimization / graded meshes / adaptivity / total variation / error estimates
© The authors. Published by EDP Sciences, SMAI 2022
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