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Structure-preserving variational schemes for nonlinear partial differential equations with a Wasserstein gradient flow structure

Presented by: 
Bertram Düring University of Sussex
Date: 
Thursday 5th December 2019 - 15:15 to 16:00
Venue: 
INI Seminar Room 2
Abstract: 
A wide range of diffusion equations can be interpreted as gradient flow with respect to Wasserstein distance of an energy functional. Examples include the heat equation, the porous medium equation, and the fourth-order Derrida-Lebowitz-Speer-Spohn equation. When it comes to solving equations of gradient flow type numerically, schemes that respect the equation's special structure are of particular interest. The gradient flow structure gives rise to a variational scheme by means of the minimising movement scheme (also called JKO scheme, after the seminal work of Jordan, Kinderlehrer and Otto) which constitutes a time-discrete minimization problem for the energy.   While the scheme has been used originally for analytical aspects, more recently a number of authors have explored the numerical potential of this scheme. In this talk we present some results on Lagrangian schemes for Wasserstein gradient flows in one spatial dimension and then discuss extensions to higher approximation order and to higher spatial dimensions




University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons