Finite Element Exterior Calculus

Catalog description

In this course we will cover finite elements for the Hodge Laplacian. We start in three dimensions and discuss the Nedelec finite element spaces for H^1, H(curl) and H(div) and discuss the corresponding de Rham complex. We discuss how they can be applied to the Stokes problem and electro-magnetic problems. We then generalize these spaces to higher dimensions and show how to use them to approximate the Hodge Laplacian. We will mostly follow the review paper: [Finite Element Exterior Calculus: from Hodge Theory to Numerical Stability].