Pointwise rates of convergence for the Oliker-Prussner method for the Monge-Amp\`{e}re equation
Numerical Analysis
2018-09-26 v2
Abstract
We study the Oliker-Prussner method exploiting its geometric nature. We derive discrete stability and continuous dependence estimates in the max-norm by using a discrete Alexandroff estimate and the Brunn-Minkowski inequality. We show that the method is exact for all convex quadratic polynomials provided the underlying set of nodes is translation invariant within the domain; nodes still conform to the domain boundary. This gives a suitable notion of operator consistency which, combined with stability, leads to pointwise rates of convergence for classical and non-classical solutions of the Monge-Amp\`{e}re equation.
Keywords
Cite
@article{arxiv.1611.02786,
title = {Pointwise rates of convergence for the Oliker-Prussner method for the Monge-Amp\`{e}re equation},
author = {Ricardo H. Nochetto and Wujun Zhang},
journal= {arXiv preprint arXiv:1611.02786},
year = {2018}
}
Comments
33 pages, 3 figures