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TPFA Finite Volume Approximation of Wasserstein Gradient Flows

Abstract : Numerous infinite dimensional dynamical systems arising in different fields have been shown to exhibit a gradient flow structure in the Wasserstein space. We construct Two Point Flux Approximation Finite Volume schemes to discretize these problems preserving their variational structure and obtaining second order accuracy in space. The choice of the discrete solver plays an important role in designing these schemes for robustness purposes. We present two applications to test the scheme and show its order of convergence.
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https://hal.archives-ouvertes.fr/hal-02444833
Contributor : Gabriele Todeschi <>
Submitted on : Sunday, January 19, 2020 - 11:49:38 AM
Last modification on : Wednesday, February 19, 2020 - 9:00:30 AM

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  • HAL Id : hal-02444833, version 1
  • ARXIV : 2001.07005

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Andrea Natale, Gabriele Todeschi. TPFA Finite Volume Approximation of Wasserstein Gradient Flows. 2020. ⟨hal-02444833⟩

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