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

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