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.

17 pages

References in corpus (1)

• Finite Element Exterior Calculus for Parabolic Evolution Problems On Riemannian Hypersurfaces

Cited by in corpus (4)

• High-order Methods for a Pressure Poisson Equation Reformulation of the Navier-Stokes Equations with Electric Boundary Conditions
• An Extended Galerkin analysis in finite element exterior calculus
• Finite Element Exterior Calculus for Evolution Problems
• Finite Element Exterior Calculus for Parabolic Evolution Problems On Riemannian Hypersurfaces