ON ADAPTIVITY FOR DIFFUSION-PROBLEMS USING TRIANGULAR ELEMENTS

In this work an adaptive scheme to solve diffusion problems, using lin ear and quadratic triangles, is presented. The densification algorithm , based on the subdivision of the selected elements, and the error est imator used are described first. We pay special attention to the behav iour of the estimator. It has two contributions: the residual term and the flux-jump term. Babuska and co-workers have shown that for biline ar quadrilterals, the first term is negligible, but for biquadratic, i t is the dominant term. We show evidence suggesting that these results cannot be extended to triangular elements when the problem has a sing ular solution. We found, in this case, that if the flux-jump term is n eglected, the expected rate of convergence cannot be obtained. Finally , some remarks about the whole adaptive process are discussed.