## View abstract

### 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. document.getElementById('cloak3ebfcc00634f0291e70cac3f87f918bf').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy3ebfcc00634f0291e70cac3f87f918bf = 'j&#111;hnny_g&#117;zm&#97;n' + '&#64;'; addy3ebfcc00634f0291e70cac3f87f918bf = addy3ebfcc00634f0291e70cac3f87f918bf + 'br&#111;wn' + '&#46;' + '&#101;d&#117;'; var addy_text3ebfcc00634f0291e70cac3f87f918bf = 'j&#111;hnny_g&#117;zm&#97;n' + '&#64;' + 'br&#111;wn' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak3ebfcc00634f0291e70cac3f87f918bf').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy3ebfcc00634f0291e70cac3f87f918bf + '\'>'+addy_text3ebfcc00634f0291e70cac3f87f918bf+'<\/a>';

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).