Some aspects of adaptive grid technology related to boundary and interior layers

Graham F. Carey, M. Anderson, B. Carnes, B. Kirk
2004 Journal of Computational and Applied Mathematics  
We consider the use of adaptive mesh strategies for solution of problems exhibiting boundary and interior layer solutions. As the presence of these layer structures suggests, reliable and accurate solution of this class of problems using ÿnite di erence, ÿnite volume or ÿnite element schemes requires grading the mesh into the layers and due attention to the associated algorithms. When the nature and structure of the layer is known, mesh grading can be achieved during the grid generation by
more » ... fying an appropriate grading function. However, in many applications the location and nature of the layer behavior is not known in advance. Consequently, adaptive mesh techniques that employ feedback from intermediate grid solutions are an appealing approach. In this paper, we provide a brief overview of the main adaptive grid strategies in the context of problems with layers. Associated error indicators that guide the reÿnement feedback control/grid optimization process are also covered and there is a brief commentary on the supporting data structure requirements. Some current issues concerning the use of stabilization in conjunction with adaptive mesh reÿnement (AMR), the question of "pollution e ects" in computation of local error indicators, the in uence of nonlinearities and the design of meshes for targeted optimization of speciÿc quantities are considered. The application of AMR for layer problems is illustrated by means of case studies from semiconductor device transport (drift di usion), nonlinear reaction-di usion, layers due to surface capillary e ects, and shockwaves in compressible gas dynamics.
doi:10.1016/j.cam.2003.09.036 fatcat:szkxrgqltjgixemhq4qh3uhwwu