PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Xiantao Li, Yuxi Zheng, Kris Jenssen, Jinchao Xu, Hope Shaffer.

Title:Geometric variational crimes: Hilbert complexes, finite element exterior calculus, and problems on hypersurfaces
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Ari Stern, UC San Diego
Abstract:
In recent years, the success of "mixed" finite element methods has been shown to have surprising connections with differential geometry and algebraic topology---particularly with the calculus of exterior differential forms, de Rham cohomology, and Hodge theory. In this talk, I will discuss how the notion of "Hilbert complex," rather than "Hilbert space," provides the appropriate functional-analytic setting for the numerical analysis of these methods. Furthermore, I will present some recent results that analyze "variational crimes" (a la Strang) on Hilbert complexes, allowing the numerical analysis to be extended from polyhedral regions in Euclidean space to problems on arbitrary Riemannian manifolds. As a direct consequence, this analysis also generalizes several key results on "surface finite element methods" for the approximation of elliptic PDEs on hypersurfaces (e.g., membranes or level sets undergoing geometric evolution).

Room Reservation Information

Room Number:MB106
Date:05 / 06 / 2011
Time:03:35pm - 04:25pm