A Parameter Robust Finite Element Method for Fourth Order Singularly Perturbed Problems

Abstract We consider fourth order singularly perturbed problems in one-dimension and the approximation of their solution by thehversion of the finite element method. In particular, we use piecewise Hermite polynomials of degree p≥3 ${p\geq 3}$ defined on anexponentially gradedmesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at the optimal rate when the error is measured in both the energy norm and a stronger, ‘balanced’ norm. Finally, we illustrate our theoretical findings through numerical computations, including a comparison with another scheme from the literature.