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 nearly linear convergence is possible on suitably constructed meshes.

翻译：对于总变差正常最小化问题的有限元素近似值,最近的近似最佳误差估计要求存在一个Lipschitz连续的双重解决方案。我们讨论这一条件的有效性,并使用当地改良的胶片设计数字方法,尽管出现不连续现象,但会提高趋同率。结果发现,在结构适当的胶片上几乎可以实现线性趋同。