Strategies for hp‐adaptive Refinement

In the hp‐adaptive version of the finite element method for solving partial differential equations, the grid is adaptively refined in both h, the size of the elements, and p, the degree of the piecewise polynomial approximation over the element. The selection of which elements to refine is determined by a local a posteriori error indicator, and is well established. But the determination of whether the element should be refined by h or p is still open. In this paper, we describe several strategies that have been proposed for making this determination. A numerical example to illustrate the effectiveness of these strategies will be presented.