Finite element exterior calculus for parabolic problems

Abstract

In this paper, we consider the extension of the finite element exterior calculus from elliptic problems, in which the Hodge Laplacian is an appropriate model problem, to parabolic problems, for which we take the Hodge heat equation as our model problem. The numerical method we study is a Galerkin method based on a mixed variational formulation and using as subspaces the same spaces of finite element differential forms which are used for elliptic problems. We analyze both the semidiscrete and a fully-discrete numerical scheme.