Computing the L1 optimal transport density: a FEM approach
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The L^1 optimal transport density μ^* is the unique L^∞ solution of the Monge-Kantorovich equations. It has been recently characterized also as the unique minimizer of the L^1 -transport energy functional E. In the present work we develop and we prove convergence of a numerical approxi- mation scheme for μ^* . Our approach relies upon the combination of a FEM- inspired variational approximation of E with a minimization algorithm based on a gradient flow method.
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