College of Liberal Arts & Sciences

# Mathematics Colloquium

**Abstract: **

A transformative trend in the last fifteen years for the discovery of better finite element methods has been the idea of compatible discretizations and the use of tools from algebraic topology and differential geometry. This program has been known as finite element exterior calculus. In this talk, we will give a unified treatment of hybrid finite element methods using finite element differential forms. This resulted in the discovery of new hybrid finite element methods, including methods for the vector Poisson equation in two and three dimensions.

Postprocessing will also be discussed. Joint work with Johnny Guzman, Maurice Fabien and Ari Stern.

*The Math Colloquium will be available live via Zoom at https://uiowa.zoom.us/j/99206823329 and recordings of the sessions will be available at https://uicapture.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx?folderID=b23b61cc-a48a-4de7-99fc-ae46015b8b6e usually within a couple hours of the colloquium finishing.

Fyi.: We usually gather on colloquium Thursdays at 2:30 pm in the common room, Muhly lounge, so folks can meet the speaker.

And after the talk we also plan colloquium dinner, usually at 6:30 pm. Everyone is welcome to all the colloquium events.