Performance of Some hp-Adaptive Strategies for 3D Elliptic Problems
The hp version of the finite element method (hp-FEM) combined with adaptive mesh refinement is a particularly efficient method for solving partial differential equations (PDEs) because it can achieve an exponential convergence rate in the number of degrees of freedom. hp-FEM allows for refinement in both the element size, h, and the polynomial degree, p. Like adaptive refinement for the h version of the finite element method, a posteriori error estimates can be used to determine where the mesh needs to be refined, but a single error estimate can not simultaneously determine whether it is better to do the refinement by h or p. Several strategies for making this determination have been proposed over the years. Recently, we presented the results of a numerical experiment to compare the performance of several hp-adaptive strategies for 2D elliptic PDEs. In this paper we present the results of a similar experiment for some of the strategies applied to 3D elliptic PDEs.