Session S20 - Applied Math and Computational Methods and Analysis across the Americas

Friday, July 16, 17:30 ~ 18:00 UTC-3

Local $L^2$ bounded commuting projections in finite element exterior calculus

Johnny Guzman

Brown University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Bounded, commuting projections are a chief tool in the analysis of finite element exterior calculus (FEEC). Such projections were originally constructed by Schoberl and Christiansen and Winther, to name a few. However, they were not local. More recently, in 2015 Falk and Winther constructed local and bounded commuting projection. They are defined for differential forms that are in $L^2$ and such that their exterior derivative is in $L^2$. Inspired by their work we construct a local and bounded commuting projection that is defined for differential forms that are in $L^2$.

Joint work with Douglas Arnold (University of Minnesota, USA).

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