Supraconvergence and supercloseness in quasilinear coupled problems

The aim of this paper is to study a finite difference method for quasilinear coupled problems of partial differential equations that presents numerically an unexpected second order convergence rate. The error analysis presented allows us to conclude that the finite difference method is supraconvergent. As the method studied in this paper can be seen as a fully discrete piecewise linear finite element method, we conclude the supercloseness of our approximations.