Rate of convergence of regularization procedures and finite element approximations for the total variation flow (Q1780605)

The paper deals with finite element approximations of the \(L^2\)-gradient flow for a total variational functional. In [M2AN, Math. Model. Numer. Anal. 37, No.3, 533--556 (2003; Zbl 1050.35004)] the authors proved that the solution of the regularized flow (characterized by a parameter \(\varepsilon\)) converges to the solution of the total variational flow. In this paper the authors derive the rate of the convergence. Practically useful error estimates, which depend on \(1/\varepsilon\) only in low polynomial orders, are established. Numerical examples verify the theoretical results and show the efficiency of the proposed methods.