In plasma physics, the electric field in a magnetised cavity is given as the solution to an anisotropic elliptic problem. When the intensity of the magnetic field is high, the situation becomes demanding, as the charged particles are nearly trapped along the magnetic field lines. From a numerical point of view, this leads to mixing different scales, damaging the numercial accuracy of the computations. However, separating scales and using differential geometry techniques allowed us to provide a reliable solution to a problem of interest, opening the way to developing reliable methods for solving these problems.