Topological Optimization and Optimal Transport 2017
DOI: 10.1515/9783110430417-015
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14. Convergence of a fully discrete variational scheme for a thin-film equation

Abstract: Abstract. This paper 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 L 2 -Wasserstein metric. Apart from its Lagrangian character -which guarantees positivity and mass conservation -the main feature of our discretization is that it dissipates both the Dirichlet energy and the logarit… Show more

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Cited by 10 publications
(11 citation statements)
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References 30 publications
(73 reference statements)
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“…Another common approach is to leverage structural similarities between (3) and equations from fluid dynamics to develop particle methods [14,27,30,36,43,48,57,60,88,92]. Until recently, the key limitation of such methods has been developing approaches to incorporate diffusion.…”
Section: Classical Numerical Pde Methodsmentioning
confidence: 99%
“…Another common approach is to leverage structural similarities between (3) and equations from fluid dynamics to develop particle methods [14,27,30,36,43,48,57,60,88,92]. Until recently, the key limitation of such methods has been developing approaches to incorporate diffusion.…”
Section: Classical Numerical Pde Methodsmentioning
confidence: 99%
“…Another common approach is to leverage structural similarities between (1.3) and equations from fluid dynamics to develop particle methods [14,25,28,34,41,46,55,58,81,85]. Until recently, the key limitation of such methods has been developing approaches to incorporate diffusion.…”
Section: Introductionmentioning
confidence: 99%
“…Our method avoids these computationally intensive procedures by the approximation of the energy in the discrete setting. Finally, note that gradient-flow-based Lagrangian methods for higher-order, drift diffusion and Fokker-Planck equations have recently been proposed in [29,30,28,22].…”
Section: Introductionmentioning
confidence: 99%