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

Jean-Luc Guermond; Luigi Quartapelle; Jiang Zhu

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 1, page 183-200
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Guermond, Jean-Luc, Quartapelle, Luigi, and Zhu, Jiang. "On a 2D vector Poisson problem with apparently mutually exclusive scalar boundary conditions." ESAIM: Mathematical Modelling and Numerical Analysis 34.1 (2010): 183-200. <http://eudml.org/doc/197483>.

@article{Guermond2010,
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. },
author = {Guermond, Jean-Luc, Quartapelle, Luigi, Zhu, Jiang},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Vector Poisson equation; mutually exclusive scalar boundary conditions; variational formulation; uncoupled solution; finite element approximation.; numerical examples; vector Poisson equation; variational formulations; splitting method; algorithm; finite element methods; error estimates},
language = {eng},
month = {3},
number = {1},
pages = {183-200},
publisher = {EDP Sciences},
title = {On a 2D vector Poisson problem with apparently mutually exclusive scalar boundary conditions},
url = {http://eudml.org/doc/197483},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Guermond, Jean-Luc
AU - Quartapelle, Luigi
AU - Zhu, Jiang
TI - On a 2D vector Poisson problem with apparently mutually exclusive scalar boundary conditions
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 1
SP - 183
EP - 200
AB - 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.
LA - eng
KW - Vector Poisson equation; mutually exclusive scalar boundary conditions; variational formulation; uncoupled solution; finite element approximation.; numerical examples; vector Poisson equation; variational formulations; splitting method; algorithm; finite element methods; error estimates
UR - http://eudml.org/doc/197483
ER -

References

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