The hp finite element method for problems in mechanics with boundary layers

We consider the numerical approximation of boundary layer phenomena occurring in many singularly perturbed problems in mechanics, such as plate and shell problems. We present guidelines for the effective resolution of such layers in the context of existing, commercial p and hp finite element (FE) version codes. We show that if high order, ‘spectral’ elements are available, then just two elements are sufficient to approximate these layers at a near-exponential rate, independently of the problem parameters thickness or Reynolds number. We present hp mesh design principles for situations where both corner singularities and boundary layers are present.