A Two-Grid Method for the C<sup>0</sup> Interior Penalty Discretization of the Monge-Ampère Equation
Year: 2020
Author: Gerard Awanou, Hengguang Li, Eric Malitz
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 4 : pp. 547–564
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-Ampère 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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1901-m2018-0039
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 4 : pp. 547–564
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Two-grid discretization Interior penalty method Finite element Monge-Ampère.