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arXiv · 1804.04279

A two-grid method for the $C^0$ interior penalty discretization of the Monge-Amp\`{e}re equation

Gerard Awanou·Hengguang Li·Eric Malitz
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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 $C^0$ 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 $W^{1,\infty}$ 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.

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Gerard Awanou, Hengguang Li, Eric Malitz. 2018-04-12. A two-grid method for the $C^0$ interior penalty discretization of the Monge-Amp\`{e}re equation. https://arxiv.org/abs/1804.04279

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