The error estimate and the convergence rate for h, p - refinement in the finite element analysis

Abstract

The goal of this study is to further investigate and to develop a more efficient way in the error estimate and the rate of the convergence for the mesh h, p-refinement procedure in the finite element analysis for two-dimensional and three-dimensional elastostatic mechanics problems. The oscillation of the stress field around singularity points is also considered in the refinement process. In this paper, a-refinement procedure with a h-uniform and p-uniform analysis capability is called a h, p-refinement procedure. We also establish the refinement criterion for the adaptive strategy with h-refinement based on the ratio of error indicator or the enrichment indicator.