A Numerical Algorithm for a fully nonlinear PDE involving the Jacobian determinant

Caboussat, Alexandre (Haute école de gestion de Genève, HES-SO // Haute Ecole Spécialisée de Suisse Occidentale) ; Glowinski, Roland (University of Houston, Texas, USA)

We address the numerical solution of the Dirichlet problem for a partial differential equation involving the Jacobian determinant in two dimensions of space. The problem consists in finding a vector-valued function such that the determinant of its gradient is given point-wise in a bounded domain, together with essential boundary conditions. The proposed numerical algorithm relies on an augmented Lagrangian algorithm with biharmonic regularization, and low order mixed finite element approximations. An iterative method allows to decouple the local nonlinearities and the global variational problem that involves a biharmonic operator. Numerical experiments validate the proposed method.


Type de conférence:
full paper
Faculté:
Economie et Services
Ecole:
HEG - Genève
Institut:
CRAG - Centre de Recherche Appliquée en Gestion
Classification:
Economie/gestion
Adresse bibliogr.:
Cham, Springer
Date:
Cham
Springer
2015
Pagination:
Pp. 143-151
Publié dans
Numerical mathematics and advanced applications - ENUMATH 2013 Proceedings of ENUMATH 2013 : the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013
DOI:
ISSN:
1439-7358
ISBN:
978-3-319-10704-2
Ressource(s) externe(s):
Le document apparaît dans:



 Notice créée le 2015-02-18, modifiée le 2018-12-07

Fichiers:
Télécharger le document
PDF

Évaluer ce document:

Rate this document:
1
2
3
 
(Pas encore évalué)