Abstract:
This thesis investigates structure-preserving, temporal semi-discretizations and approximations for PDEs with gradient flow structure with the application to evolution problems in the L²-Wasserstein space. We investigate the variational formulation of the time-dependent Minimizing Movement scheme, the second order Backward Differentiation Formula, and the Weighted Energy-Dissipation principle. The two examples of application are the non-linear Fokker-Planck equation and the DLSS equation.