On adaptivity for diffusion problems using triangular elements Available to Purchase

In this work an adaptive scheme to solve diffusion problems, using linear and quadratic triangles, is presented. The densification algorithm,based on the subdivision of the selected elements, and the error estimator used are described first. We pay special attention to the behaviour of the estimator. It has two contributions: the residual term and the flux‐jump term. Babuska and co‐workers have shown that for bilinear quadrilterals, the first term is negligible, but for biquadratic, it is the dominant term. We show evidence suggesting that these results cannot be extended to triangular elements when the problem has a singular solution. We found, in this case, that if the flux‐jump term is neglected, the expected rate of convergence cannot be obtained. Finally, some remarks about the whole adaptive process are discussed.