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.
Accepté le :
DOI : 10.1051/m2an/2016013
Mots-clés : Finite element exterior calculus, mixed finite element method, parabolic equation, Hodge heat equation
@article{M2AN_2017__51_1_17_0,
author = {Arnold, Douglas N. and Chen, Hongtao},
title = {Finite element exterior calculus for parabolic problems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {17--34},
publisher = {EDP-Sciences},
volume = {51},
number = {1},
year = {2017},
doi = {10.1051/m2an/2016013},
mrnumber = {3600999},
zbl = {1362.65100},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2016013/}
}
TY - JOUR AU - Arnold, Douglas N. AU - Chen, Hongtao TI - Finite element exterior calculus for parabolic problems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 17 EP - 34 VL - 51 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016013/ DO - 10.1051/m2an/2016013 LA - en ID - M2AN_2017__51_1_17_0 ER -
%0 Journal Article %A Arnold, Douglas N. %A Chen, Hongtao %T Finite element exterior calculus for parabolic problems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 17-34 %V 51 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016013/ %R 10.1051/m2an/2016013 %G en %F M2AN_2017__51_1_17_0
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. http://www.numdam.org/articles/10.1051/m2an/2016013/
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