Residual-based a posteriori error estimates for a conforming mixed finite element discretization of the Monge-Amp\`ere equation
Numerical Analysis
2019-12-06 v1 Numerical Analysis
Abstract
In this paper we develop a new a posteriori error analysis for the Monge-Amp\`ere equation approximated by conforming finite element method on isotropic meshes in 2D. The approach utilizes a slight variant of the mixed discretization proposed by Gerard Awanou and Hengguang Li in International Journal of Numerical Analysis and Modeling, 11(4):745-761, 2014. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.
Keywords
Cite
@article{arxiv.1912.02690,
title = {Residual-based a posteriori error estimates for a conforming mixed finite element discretization of the Monge-Amp\`ere equation},
author = {Jamal Adetola and Koffi Wilfrid Houedanou and Bernardin Ahounou},
journal= {arXiv preprint arXiv:1912.02690},
year = {2019}
}
Comments
12 Page, 03 figures. arXiv admin note: text overlap with arXiv:1703.01755