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In this paper we develop a new a posteriori error analysis for theMonge-Amp\`ere equation approximated by conforming finite element method onisotropic meshes in 2D. The approach utilizes a slight variant of the mixeddiscretization proposed by Gerard Awanou and Hengguang Li in InternationalJournal of Numerical Analysis and Modeling, 11(4):745-761, 2014. The aposteriori error estimate is based on a suitable evaluation on the residual ofthe finite element solution. It is proven that the a posteriori error estimateprovided in this paper is both reliable and efficient.

Residual-based a posteriori error estimates for a conforming mixed finite element discretization of the Monge-Amp\`ere equation