The p and hp finite element method for problems on thin domains

The p and hp versions of the finite element method allow the user to change the polynomial degree to increase accuracy. We survey these methods and show how this flexibility can be exploited to counter four difficulties that occur in the approximation of problems over thin domains, such as plates, beams and shells. These difficulties are: (1) control of modeling error, (2) approximation of corner singularities, (3) resolution of boundary layers, and (4) control of locking. Our guidelines enable the efficient resolution of these difficulties when a p/hp code is available.