3rd Year Candidacy Requirement: HDG Methods, M-Decompositions, and Finite Element Exterior Calculus

Abstract: We consider various types of finite element methods, using the primal and mixed formulations of the scalar Poisson equation as model problems. In particular, we consider conforming methods and hybridizable discontinuous Galerkin (HDG) methods. In both these cases, projections onto the discrete spaces involved have enabled an analysis that yields desirable error estimates. Finite element exterior calculus, or FEEC, unifies many approaches under a single framework. Current research focuses on expanding the work that has been done on projections to FEEC HDG methods.

Advisor: Ari Stern