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. | Vietnam Journal of Mechanics, VAST, Vol. 30, No. 3 (2008), pp. 179 – 184 THE ERROR ESTIMATE AND THE CONVERGENCE RATE FOR h, p - REFINEMENT IN THE FINITE ELEMENT ANALYSIS Nguyen Hoai Son University of Technical Education, Hochiminh City 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. Keywords Estimate, refinement, error indicator. 1. INTRODUCTION In this paper, a-refinement procedure with a h-uniform and p-uniform analysis capability is called h, p-refinement procedure. We have established a criterion for refinement procedure in the error estimate and the rate of convergence based on the ratio of error indicator. Several error estimates have been developed for engineering use. However, they are computationally intensive and still need to be validated for accuracy in practical engineering analysis [1, 3, 6]. Besides, the mentioned error estimates are in the form of an energy norm. This quantity differs from the quantities of interest in solid mechanics analysis, which are usually displacements or stresses at particular points inside a problem domain. Also, the energy convergence may not guarantee stress convergence. The development of an accurate error estimate for stress will result in a more efficient way of controlling the refinement process [2, 4, 7] and will provide valuable information for checking the convergence of final stress .
