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.


Conference Type:
full paper
Faculty:
Economie et Services
School:
HEG - Genève
Institute:
CRAG - Centre de Recherche Appliquée en Gestion
Subject(s):
Economie/gestion
Publisher:
Cham, Springer
Date:
Cham
Springer
2015
Pagination:
Pp. 143-151
Published in:
Numerical mathematics and advanced applications - ENUMATH 2013 Proceedings of ENUMATH 2013 : the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013
Series Statement:
Lecture Notes in Computational Science and Engineering, vol. 103
DOI:
ISSN:
1439-7358
ISBN:
978-3-319-10704-2
External resources:
Appears in Collection:



 Record created 2015-02-18, last modified 2019-06-11

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