An Adaptive Mesh Refinement for the Finite Element Method. 3rd Report. Convergence at h-Global Remeshing Scheme.

Abstract

Since the quality of FEM analysis directly depends on the quality of meshes, various mesh adaptation schemes have been studied. There are two stages in adaptive mesh refinement: to derive error measure and to control meshes according to error estimation. The former has been well researched. However, the importance of the latter aspect has not been adequately considered. Even if the error measure is well estimated, the total performance of mesh adaptation might be poor with poor mesh control. We provided an effective remeshing scheme in the previous paper, although the desirable mesh size was not well derived there. In this paper, the explicit relation between error measure and mesh size is proposed. After evaluation on several examples, it is confirmed that the proposed error measure-mesh size relation is acceptable. The limitation of mesh adaptation is also discussed in this paper.