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Simplifying numerical solution of constrained PDE systems through involutive completion

Published online by Cambridge University Press:  15 September 2005

Bijan Mohammadi  and
Jukka Tuomela
Bijan Mohammadi
Affiliation:
Mathematics and Modeling Institute, Montpellier University, France and Department of Mathematics, University of Joensuu, PO Box 111, 80101 Joensuu, Finland. bijan.mohammadi@math.univ-montp2.fr; jukka.tuomela@joensuu.fi
Jukka Tuomela
Affiliation:
Mathematics and Modeling Institute, Montpellier University, France and Department of Mathematics, University of Joensuu, PO Box 111, 80101 Joensuu, Finland. bijan.mohammadi@math.univ-montp2.fr; jukka.tuomela@joensuu.fi
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Abstract

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 PDEsinvolutiondiscretization.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 5 , September 2005 , pp. 909 - 929
Copyright
© EDP Sciences, SMAI, 2005

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