# 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

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topGuermond, 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 -

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