Pacific Northwest Numerical Analysis Seminar

Abstracts

This talk presents a relatively new class of finite element methods, called Hybridizable Discontinuous Galerkin (HDG) methods. While finite element methods have long been indispensable in the numerical solution of boundary value problems on complex structures, there is a resurgence of interest in the `hybridized' variety. Hybridization, in the finite element context, is the process of formulating methods that exploit interface unknowns, i.e., variables at the interfaces of mesh elements. Interface unknowns can be used, in a transparent fashion, to reduce system size, and in a more subtle fashion, to obtain stable high order methods. Beginning with standard domain decomposition ideas, we will arrive at concepts in hybridized finite elements, HDG methods, and hybridized eigenvalue problems.