Peter K. Moore ¹

Designing efective high-order adaptive methods for solving stationary reaction-diffusion equations in three dimensions requires the selection of a finite element basis, a postscript error estimator and refinement strategy. Estimator accuracy may depend on the basis chosen, which in turn, may lead to unreliability or inefficiency via under- or over-refinement, respectively. The basis may also have an impact on the size and conditon of the matrices that arise from discretization, and thus, on algorithm effectiveness. Herein, the interaction between these three components is studied in the context of an h-refinement prcedure. The effects of these choices on the robustness and efficiency of the algorithm are examined for several linear and nonlinear problems. The results demonstrate that popular choices such as the tensor-product basis or the modified Szabo-Babuska basis have significant shortcomings but that promising alternatives exist.