A convergent Lagrangian discretization for a nonlinear fourth order equation

Understand

A fully discrete Lagrangian scheme for numerical solution of the nonlinear fourth order DLSS equation in one space dimension is analyzed.

• The discretization is based on the equation's gradient flow structure in the $L^2$-Wasserstein metric.
• We prove that the discrete solutions are strictly positive and mass conserving.
• Further, they dissipate both the Fisher information and the logarithmic entropy.