Paper Info
Title
Numerical solution of the Dirichlet problem for a Pucci equation in dimension two. Application to homogenization
Abstract
The main goal of this article is two fold: (i) To discuss a methodology for the numerical solution of the Dirichlet problem for a Pucci equation in dimension two. (ii) Use the ensuing algorithms to investigate the homogenization properties of the solutions when a coefficient in the Pucci equation oscillates periodically or randomly in space. The solution methodology relies on the combination of a least-squares formulation of the Pucci equation in an appropriate Hilbert space with operator-splitting techniques and mixed finite element approximations. The results of numerical experiments suggest second order accuracy when globally continuous piecewise affine space approximations are used; they also show that the solution of the problem under consideration can be reduced to a sequence of discrete Poisson-Dirichlet problems coupled with one-dimensional optimization problems (one per grid point).
Year
DOI
Venue
2008
10.1515/JNUM.2008.009
JOURNAL OF NUMERICAL MATHEMATICS
Keywords
DocType
Volume
Fully nonlinear elliptic equations,nonlinear least squares,finite element approximation,homogenization
Journal
16
Issue
ISSN
Citations 
3
1570-2820
4
PageRank 
References 
Authors
0.47
0
2
Name
Order
Citations
PageRank
Luis Caffarelli140.47
Roland Glowinski218850.44