Adaptive finite element computational fluid dynamics using an anisotropic error estimator

The aim of this paper is to present the results on finite element adaptive strategies for computational fluid dynamics (CFD) problems with singulariti es arising from shock phenomena and/or discontinuous boundary data. The ada ptive analysis is based on an optimal-mesh-adaptive strategy which is emplo yed to refine the mesh, stretch and orient the elements in such a way that, along the adaptation process, the mesh becomes aligned with the discontinu ities. This mesh adaptation process yields improved results in locating reg ions of rapid or abrupt variations of the variables, whose location is not known a priori. On the other hand, the proposed mesh adaptation process is generated by minimizing, for a given number of elements in the mesh, a new anisotropic error estimator based on local directional interpolation error and recovering of the second derivatives of the finite element solution. Se veral adaptive mesh-refinement solutions for interpolation problems are pre sented in order to show that the proposed optimal adaptive strategy using t his anisotropic error estimator recovers optimal and/or superconvergent rat es. Finally, applications of this approach to CFD problems are also present ed in order to show the computational performance of the proposed optimal a daptive procedure. (C) 2000 Elsevier Science S.A. All rights reserved.