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arXiv · 2201.04055

Error estimates for total-variation regularized minimization problems with singular dual solutions

Alex Kaltenbach·Sören Bartels
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Abstract

Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems using the Crouzeix--Raviart finite element require the existence of a Lipschitz continuous dual solution, which is not generally given. We provide analytic proofs showing that the Lipschitz continuity of a dual solution is not necessary, in general. Using the Lipschitz truncation technique, we, in addition, derive error estimates that depend directly on the Sobolev regularity of a given dual solution.

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Alex Kaltenbach, Sören Bartels. 2022-01-11. Error estimates for total-variation regularized minimization problems with singular dual solutions. https://arxiv.org/abs/2201.04055

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