A two-grid method for the $C^0$ interior penalty discretization of the Monge-Amp\`{e}re equation
Abstract
The purpose of this paper is to analyze an efficient method for the solution of the nonlinear system resulting from the discretization of the elliptic Monge-Amp\`ere equation by a interior penalty method with Lagrange finite elements. We consider the two-grid method for nonlinear equations which consists in solving the discrete nonlinear system on a coarse mesh and using that solution as initial guess for one iteration of Newton's method on a finer mesh. Thus both steps are inexpensive. We give quasi-optimal error estimates for the discretization and estimate the difference between the interior penalty solution and the two-grid numerical solution. Numerical experiments confirm the computational efficiency of the approach compared to Newton's method on the fine mesh.
Keywords
Cite
@article{arxiv.1804.04279,
title = {A two-grid method for the $C^0$ interior penalty discretization of the Monge-Amp\`{e}re equation},
author = {Gerard Awanou and Hengguang Li and Eric Malitz},
journal= {arXiv preprint arXiv:1804.04279},
year = {2018}
}