A Petrov–Galerkin multilayer discretization to second order elliptic boundary value problems

We study in this paper a multilayer discretization of second order elliptic problems, aimed at providing reliable multilayer discretizations of shallow fluid flow problems with diffusive effects. This discretization is based upon the formulation by transposition of the equations. It is a Petrov–Galerkin discretization in which the trial functions are piecewise constant per horizontal layers, while the test functions are continuous piecewise linear, on a vertically shifted grid.