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Topological Optimization and Optimal Transport by Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux

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Horst Osberger and Daniel Matthes

14 Convergence of a fully discrete variational scheme for a thin-film equation

Horst Osberger, Horst Osberger, Zentrum Mathematik, TU München, Boltzmannstr. 3, D-85748 Garching, Germany, osberger@ma.tum.de

Daniel Matthes, Daniel Matthes, Zentrum Mathematik, TU München, Boltzmannstr. 3, D-85748 Garching, Germany, matthes@ma.tum.de

Abstract: This chapter is concerned with a rigorous convergence analysis of a fully discrete Lagrangian scheme for the Hele–Shaw flow, which is the fourth-order thin-film equation with linear mobility in one space dimension. The discretization is based on the equation’s gradient flow structure in the L2-Wasserstein metric. Apart from its Lagrangian character – which guarantees positivity ...

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