Geodesic
Finite element exterior calculus for parabolic problems
Arnold, Douglas N.1  ; Chen, Hongtao2
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.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 17-34

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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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2016013
Classification : 65N30
Keywords: Finite element exterior calculus, mixed finite element method, parabolic equation, Hodge heat equation

Arnold, Douglas N. 1 ; Chen, Hongtao 2

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. 
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Arnold, Douglas N.; Chen, Hongtao. Finite element exterior calculus for parabolic problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 17-34. doi: 10.1051/m2an/2016013

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