Total variation flow ($u_t\in -\partial \mathrm{TV}(u)$)

Total variation flow is the $L^2$ gradient flow of the total variation seminorm on a domain. Formally it is $u_t=\mathrm{div}(\nabla u/|\nabla u|)$, but the subgradient formulation handles zero gradients and jumps. Adding quadratic fidelity gives a strictly convex stationary total variation denoising problem.