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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. (guermond@limsi.fr)
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. (jiang@lncc.br)
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Abstract

This work is devoted to the study of a two-dimensional vector Poisson equation with the normal component of the unknown and the value of the divergence of the unknown prescribed simultaneously on the entire boundary. These two scalar boundary conditions appear prima facie alternative in a standard variational framework. An original variational formulation of this boundary value problem is proposed here. Furthermore, an uncoupled solution algorithm is introduced together with its finite element approximation. The numerical scheme has been implemented and applied to solve a simple test problem.

Keywords

Vector Poisson equationmutually exclusive scalar boundary 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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