Least-squares/relaxation method for the numerical solution of a 2D Pucci’s equation

Caboussat, Alexandre (Haute école de gestion de Genève, HES-SO // Haute Ecole Spécialisée de Suisse Occidentale)

The numerical solution of the Dirichlet problem for an elliptic Pucci’s equation in two dimensions of space is addressed by using a least-squares approach. The algorithm relies on an iterative relaxation method that decouples a variational linear elliptic PDE problem from the local nonlinearities. The approximation method relies on mixed low order finite element methods. The least-squares framework allows to revisit and extend the approach and the results presented in [Caffarelli, Glowinski, 2008] to more general cases. Numerical results show the convergence of the iterative sequence to the exact solution, when such a solution exists. The robustness of the approach is highlighted, when dealing with various types of meshes, domains with curved boundaries, nonconvex domains, or non-smooth solutions.


Article Type:
scientifique
Faculty:
Economie et Services
School:
HEG - Genève
Institute:
CRAG - Centre de Recherche Appliquée en Gestion
Subject(s):
Economie/gestion
Date:
2019-12
Pagination:
20 p.
Published in:
Methods and applications of analysis
Numeration (vol. no.):
2019, vol. 26, no 2, pp. 113-132
DOI:
ISSN:
1073-2772
Appears in Collection:



 Record created 2020-04-15, last modified 2020-10-27

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