Séance Séminaire

Numerical Algebraic Geometry and Algebraic Numerical Analysis

jeudi 04 avril 2019 à 14h30 - 430

Daniele Boffi ()

From the finite element method to the finite element exterior calculus

The finite element exterior calculus (FEEC) has been developed in the early 2000s as a mathematical framework that uses the calculus of differential forms for the formulation of the finite element method. The aim of this lecture is to revisit some of the main aspects of FEEC. We shall use as a main motivation the approximation of Laplace equation in mixed form and of the time harmonic formulation of Maxwell's equations. It is remarkable that, besides providing a more elegant and comprehensive understanding of the existing theory, the FEEC allows for the development of new finite elements and for the solution of problems that would be difficult, if not impossible, to address with more traditional tools.