Analysis of Total Variation Flow and Its Finite Element Approximations

  title={Analysis of Total Variation Flow and Its Finite Element Approximations},
  author={Xiaobing Feng and Andreas Prohl},
We study the gradient flow for the total variation functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow, and establish well-posedness of the problem by the energy method. The main idea of our approach is to exploit the relationship between the regularized gradient flow (characterized by a small positive parameter ε, see (1.7)) and the minimal surface flow [21] and the prescribed mean curvature flow… CONTINUE READING


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