Geometry & Topology Seminar: "Finite element methods, symmetry invariance, and conservation laws"
Yasha Berchenko-Kogan, Washington University in Saint Louis
Abstract: One of the challenges in numerical analysis is to set up the numerical discretization in a way that respects the symmetries present in the original problem. Doing so results in a numerical method that preserves conserved quantities, such as momentum or energy, for all time. In joint work with Ari Stern, we are developing a hybrid finite element method for solving Maxwell's equations, and more generally the Yang-Mills equations, in a way that respects the gauge symmetry and hence gives a numerical method that satisfies the law of charge conservation.
Using Laplace's equation as an example, I will give an expository introduction to finite element methods and hybrid finite element methods. Then I will describe how Ari and I are able to apply these methods to Maxwell's equations to create a numerical method that respects the gauge symmetry.
Host: Xiang Tang