Visiting Scholars Seminar Series
Please join us on April 19, from noon to 2pm in Donovan Hall Room G152 to hear Dr. Holger Heumann speak on " Lagrangian and Eulerian Methods for Generalized Advection-Diffusion". Dr. Heumann will lecture by invitation of Dr. Andrea Dziubek and Dr. Edmond Rusjan. Light refreshments will be served.
"We study stationary and transient advection diffusion
for differential forms and their Lagrangian and Eulerian
discretization by means of discrete differential forms.
discrete differential forms provide models both for the classical scalar advection diffusion equation, as well as for the transport of magnetic fields in moving conducting fluids (magnetohydrodynamics). The challenge is robustness and optimal a priori error estimates in the case of vanishing diffusion. Exterior calculus involving the Lie derivative will be harnessed to achieve streamlined formulations and sharper a priori convergence estimates."
About the Speaker
"Holger Heumann received his PhD in Mathematics from Swiss Federal Institute of Technology in Zurich (ETH) in 2011, where he developed and implemented efficient multi-grid methods or stable mixed finite element methods for magnetohydrodynamics. For this he used exterior calculus of differential forms, a coordinate-free approach to multivariable calculus invented by E. Cartan a century ago, which offers a unified approach to integration over curves, surfaces and higher dimensional manifolds, and has recently received much attention in the construction of structure preserving numerical methods.
At the LRC Fusion in Nice (France) he contributed to the development of software for plasma and nuclear fusion simulations. Currently he is a visiting professor at Rutgers University (NJ).
Dr. Heumann works with experts (Ralf Hiptmair, Jacques Blum, Michael Vogelius), he was an Oberwolfach Leibniz graduate student, and was awarded a fellowship by the Chinese University of Hong Kong. He was also the lead developer of LehrFEM, a Matlab finite element library for teaching numerical mathematics."