Abstract
We present an hp Finite Element Method (FEM) for the approximation to the solution of singularly perturbed fourth order problems in one-dimension. In (Panaseti et al, Appl Numer Math 104:81–97, 2016) it was shown that the hp version of the FEM, on the so-called Spectral Boundary Layer Mesh (Melenk et al, IMA J Numer Anal 33(2):609–628, 2013) yields robust exponential convergence when the error is measured in the energy norm. This result is sharpened by showing that the same method gives robust exponential convergence in a stronger, more balanced norm. As a corollary, we also get exponential convergence in the maximum norm. A numerical example illustrating the theory is also presented.
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