An hp finite element method for a 4th order singularly perturbed boundary value problem in two dimensions

We consider a fourth order singularly perturbed boundary value problem posed in a square and the approximation of its solution by the hp version of the finite element method on the so-called Spectral Boundary Layer mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at an exponential rate when the error is measured in the energy norm. Our theoretical findings are illustrated through a numerical example.