Finite Element Exterior Calculus

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].