When analysing general systems of PDEs, it is important first to find the involutive form of the initial system. This is because the properties of the system cannot in general be determined if the system is not involutive. We show that the notion of involutivity is also interesting from the numerical point of view. The use of the involutive form of the system allows one to consider quite general situations in a unified way. We illustrate our approach on the numerical solution of several flow equations with the aim of showing the impact of the involutive form of the systems in simplifying numerical schemes.
Keywords: overdetermined PDEs, involution, discretization
@article{M2AN_2005__39_5_909_0,
author = {Mohammadi, Bijan and Tuomela, Jukka},
title = {Simplifying numerical solution of constrained {PDE} systems through involutive completion},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {909--929},
publisher = {EDP-Sciences},
volume = {39},
number = {5},
year = {2005},
doi = {10.1051/m2an:2005040},
zbl = {1078.35010},
mrnumber = {2178567},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2005040/}
}
TY - JOUR AU - Mohammadi, Bijan AU - Tuomela, Jukka TI - Simplifying numerical solution of constrained PDE systems through involutive completion JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2005 SP - 909 EP - 929 VL - 39 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2005040/ DO - 10.1051/m2an:2005040 LA - en ID - M2AN_2005__39_5_909_0 ER -
%0 Journal Article %A Mohammadi, Bijan %A Tuomela, Jukka %T Simplifying numerical solution of constrained PDE systems through involutive completion %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2005 %P 909-929 %V 39 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2005040/ %R 10.1051/m2an:2005040 %G en %F M2AN_2005__39_5_909_0
Mohammadi, Bijan; Tuomela, Jukka. Simplifying numerical solution of constrained PDE systems through involutive completion. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 (2005) no. 5, pp. 909-929. doi : 10.1051/m2an:2005040. http://www.numdam.org/articles/10.1051/m2an:2005040/
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