Can I read A BDF2-Approach for the Non-linear Fokker-Planck Equation on EtoBox?

A BDF2-Approach for the Non-linear Fokker-Planck Equation by Plazotta, Simon is a scholarly article available to read on EtoBox.

What is A BDF2-Approach for the Non-linear Fokker-Planck Equation about?

We prove convergence of a variational formulation of the BDF2 method applied to the non-linear Fokker-Planck equation. Our approach is inspired by the JKO-method and exploits the differential structure of the underlying $L^2$-Wasserstein space. The technique presented here extends and strengthens the results of our own recent work on the BDF2 method for general metric gradient flows in the special case of the non-linear Fokker-Planck equation: firstly, we do not require uniform semi-convexity of the augmented energy functional; secondly, we prove strong instead of merely weak convergence of the time-discrete approximations; thirdly, we directly prove without using the abstract theory of curves of maximal slope that the obtained limit curve is a weak solution of the non-linear Fokker-Planck equation.

Author

Plazotta, Simon

Published

2018

Language

EN