On a 2D vector Poisson problem with apparently mutually exclusive scalar boundary conditions
Laboratoire d'Informatique pour la Mécanique et
les Sciences de l'Ingénieur,
CNRS, BP 133,
91403 Orsay, France. (email@example.com)
2 Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy.
3 Laboratório Nacional de Computação Científica, MCT, Avenida Getúlio Vargas 333, Petrópolis, 25651-070 RJ, Brazil. (firstname.lastname@example.org)
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.
Mathematics Subject Classification: 35J20 / 35Q / 65N30 / 76
Key words: Vector Poisson equation / mutually exclusive scalar boundary conditions / variational formulation / uncoupled solution / finite element approximation.
© EDP Sciences, SMAI, 2000