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On a 2D vector Poisson problem with apparently mutually exclusive scalar boundary conditions

Published online by Cambridge University Press:  15 April 2002

Jean-Luc Guermond ,
Luigi Quartapelle  and
Jiang Zhu
Jean-Luc Guermond
Affiliation:
Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur, CNRS, BP 133, 91403 Orsay, France. ([email protected])
Luigi Quartapelle
Affiliation:
Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy.
Jiang Zhu
Affiliation:
Laboratório Nacional de Computação Científica, MCT, Avenida Getúlio Vargas 333, Petrópolis, 25651-070 RJ, Brazil. ([email protected])
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Abstract

This work is devoted to the study of a two-dimensional vectorPoisson equation with the normal component of the unknown andthe value of the divergence of the unknown prescribed simultaneouslyon the entire boundary.These two scalar boundary conditions appear prima faciealternative in a standard variational framework. An originalvariational formulation of this boundary value problemis proposed here. Furthermore, an uncoupled solution algorithm isintroduced together with its finite element approximation.The numerical scheme has been implemented and appliedto solve a simple test problem.

Keywords

Vector Poisson equationmutually exclusive scalarboundary conditionsvariational formulationuncoupled solutionfinite element approximation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 1 , January 2000 , pp. 183 - 200
Copyright
© EDP Sciences, SMAI, 2000

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