Award for Simon Plazotta
12. AIMS Conference in July 2018 in Taipei
Outstanding student research: Simon Plazotta receives an award for his paper "A BDF2 approach for the non-linear Fokker-Planck equation". He is one of the best at the AIMS Conference 2018 Student Paper Competition.
From 5 to 9 July, 2018, the American Institute of Mathematical Sciences (AIMS) hosted the Conference on Dynamical Systems and Differential Equations in Taipei, Taiwan. At the conference banquet on 7 July, the selection committee awarded the prizes for the best papers. Plazotta has convinced the jury with his abstract and his presentation, prevails among 30 competitors and achieves third place among the 10 finalists.
A BDF2-approach for the non-linear Fokker-Planck equation
The paper A BDF2-approach for the non-linear Fokker-Planck equation deals with the numerical method Backward-Differentiation-Formula 2 (BDF2) applied to the class of non-linear Fokker-Planck equations. For example, these differential equations model the temporal dynamics of diffusion and the aggregation of gases in physics.
The focus is on the approximation of the solution of the differential equations, so that certain properties of the dynamics - the gradient flux structure - are retained in the numerical process. A clever (variational) formulation of the numerical method allows constructing approximations and proving their convergence against the original solution.
Structure Preserving Discretization of Gradient Flows
Simon Plazotta is a doctoral candidate of Prof. Daniel Matthes and represents the scientific staff in the Board of the Department of Mathematics.
His dissertation "Structur preserving discretization and apporximation of gradient flows in water stone-like spaces" is funded by the DFG Collaborative Research Center TRR 109. The subproject B09 "Structure Preserving Discretization of Gradient Flows" aims to clarify how to discretize certain differential equations so that the computation gets physical properties.
For more information about the conference in Taipei, see AIMS Conference 2018.