Finite Element Exterior Calculus with Smoother Spaces

Abstract: Finite element methods are an important class of methods to numerically approximate solutions to partial differential equations. About twenty years ago the finite element exterior calculus (FEEC) emerged and uses the language of differential forms to unify the analysis finite element methods for different important problems. In the core of FEEC are piecewise polynomial spaces that are related to the spaces used by Whitney in his proof of de Rhams' theorem (an important result in topology). Those spaces are not very smooth, however, in several applications smoother spaces are more natural. We discuss some new, smoother piecewise polynomial spaces that have been developed.

commutative algebraalgebraic geometrygeneral mathematicsnumber theoryrings and algebras

Audience: undergraduates

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PRiME: Pomona Research in Mathematics Experience

Series comments: PRiME is hosting a series of talks which will take place on Fridays in July. All are welcome to join us either in person at Pomona College or virtually over Zoom. There will be two types of series.

PROFESSIONAL DEVELOPMENT WORKSHOPS

We will have a series of 2-hour workshops geared for undergraduate students, graduate students, and faculty. The Morning Sessions will take place from 10:00 AM - 12:00 PM Pacific, while the Afternoon Sessions will take place from 2:00 PM - 4:00 PM Pacific. The Student Professional Development Series (geared for undergraduates) will meet at Pomona College in Estella 1051 (Argue Auditorium); while the Faculty Professional Development Series (geared for graduate students and junior faculty) will meet in Estella 1021 (Noether Auditorium).

COLLOQUIUM SERIES

We will have outside speakers to visit with us on Fridays from 4:30 PM - 6:00 PM Pacific. We will meet in person at Pomona College in Estella 1051 (Argue Auditorium).

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