# Simplifying numerical solution of constrained PDE systems through involutive completion

Bijan Mohammadi; Jukka Tuomela

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 39, Issue: 5, page 909-929
- ISSN: 0764-583X

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topMohammadi, Bijan, and Tuomela, Jukka. "Simplifying numerical solution of constrained PDE systems through involutive completion." ESAIM: Mathematical Modelling and Numerical Analysis 39.5 (2010): 909-929. <http://eudml.org/doc/194293>.

@article{Mohammadi2010,

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.
},

author = {Mohammadi, Bijan, Tuomela, Jukka},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Overdetermined PDEs; involution; discretization.; elliptic systems; involutive form; overdetermined systems; discretization; auxiliary variables},

language = {eng},

month = {3},

number = {5},

pages = {909-929},

publisher = {EDP Sciences},

title = {Simplifying numerical solution of constrained PDE systems through involutive completion},

url = {http://eudml.org/doc/194293},

volume = {39},

year = {2010},

}

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

DA - 2010/3//

PB - EDP Sciences

VL - 39

IS - 5

SP - 909

EP - 929

AB -
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.

LA - eng

KW - Overdetermined PDEs; involution; discretization.; elliptic systems; involutive form; overdetermined systems; discretization; auxiliary variables

UR - http://eudml.org/doc/194293

ER -

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