Simplifying numerical solution of constrained PDE systems through involutive completion
Mathematics and Modeling Institute, Montpellier University, France
Department of Mathematics,
University of Joensuu, PO Box 111, 80101 Joensuu, Finland.
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.
Mathematics Subject Classification: 35G15 / 35N10 / 65M60 / 65N30
Key words: Overdetermined PDEs / involution / discretization.
© EDP Sciences, SMAI, 2005