1 School of Mathematics, University of Minnesota, Minneapolis,
MN 55455. USA.
2 School of Mathematical Sciences, Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen 361005, P.R. China.
Corresponding author firstname.lastname@example.org
Revised: 7 December 2015
Accepted: 2 February 2016
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.
Mathematics Subject Classification: 65N30
Key words: Finite element exterior calculus / mixed finite element method / parabolic equation / Hodge heat equation
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.
© EDP Sciences, SMAI 2016