Department of Mathematics, Statistics, and Computer Science
M/C 249. University of Illinois at Chicago
Chicago, IL 60607-7045, USA
email: awanou@uic.edu
Gerard Awanou
Abstract:
We make two relaxations of the Oliker-Prussner method for the Dirichlet problem for
the Monge-Ampere equation. First we relax the convexity requirement and consider
mesh functions which are only discrete convex. The second relaxation consists in
using a finite stencil. The discrete nonlinear equations are solved with a damped
Newton's method. We give two proofs of convergence of the resulting scheme for
right-hand side a density, on domains which are convex and not necessarily strictly
convex, under the assumption that the boundary data has a continuous convex extension.
The first proof is based on the notion of Aleksandrov solution while the second uses
viscosity solutions.
Published August 25, 2022.
Math Subject Classifications: 39A12, 35J60, 65N12, 65M06.
Key Words: Discrete Monge-Ampere; Aleksandrov solution; weak convergence of measures.
DOI: https://doi.org/10.58997/ejde.conf.26.a2
Show me the PDF file (380 K), TEX file for this article.
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Gerard Awanou Department of Mathematics, Statistics, and Computer Science M/C 249. University of Illinois at Chicago Chicago, IL 60607-7045, USA email: awanou@uic.edu |
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