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 that are used for elliptic problems. We analyze both the semidiscrete and a fully-discrete numerical scheme.
|Original language||English (US)|
|Number of pages||18|
|Journal||ESAIM: Mathematical Modelling and Numerical Analysis|
|State||Published - Jan 1 2017|
Bibliographical noteFunding Information:
The work of the first author was supported in part by NSF Grant DMS-1418805. The work of the corresponding author was supported in part by the National Natural Science Foundation of China under Grant 11301437, the Natural Science Foundation of Fujian Province of China under Grant 2013J05015, and the Fundamental Research Funds for the Central Universities under grant 20720150004.
- Finite element exterior calculus
- Hodge heat equation
- Mixed finite element method
- Parabolic equation