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.

Classification: 35G15, 35N10, 65M60, 65N30

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 - Mod\'elisation Math\'ematique et Analyse Num\'erique}, publisher = {EDP-Sciences}, volume = {39}, number = {5}, year = {2005}, pages = {909-929}, doi = {10.1051/m2an:2005040}, zbl = {1078.35010}, mrnumber = {2178567}, language = {en}, url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 5, pp. 909-929. doi : 10.1051/m2an:2005040. http://www.numdam.org/item/M2AN_2005__39_5_909_0/

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