Speaker: Ari Stern, WUSTL

Title: Structure-preserving hybrid finite element methods

Abstract: The classical finite element method uses piecewise-polynomial function spaces satisfying continuity and boundary conditions. Hybrid finite element methods, by contrast, drop these continuity and boundary conditions from the function spaces and instead enforce them weakly using Lagrange multipliers. The hybrid approach has several numerical and implementational advantages, which have been studied over the last few decades.

In this talk, we show how the hybrid perspective has yielded new insights—and new methods—in structure-preserving numerical PDEs. These include multisymplectic methods for Hamiltonian PDEs, charge-conserving methods for the Maxwell and Yang-Mills equations, and hybrid methods in finite element exterior calculus.

Bio: Ari Stern is an Associate Professor of Mathematics and Statistics Washington University in St. Louis. He received his B.A. and M.A. from the mathematics department at Columbia University. In 2009, he received his  Ph.D. in Applied and Computational Mathematics at Caltech, under the direction of the late Jerrold E. Marsden and Mathieu Desbrun. Before arriving at WashU in 2012, he was a postdoc in the mathematics department at UCSD, where he worked with Michael Holst.