Residual-based a posteriori error estimates for a conforming mixed finite element discretization of the Monge-Ampère equation
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In this paper we develop a new a posteriori error analysis for the Monge-Ampère 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.
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