A Modification in the Richardson’s Extrapolation in Error Estimate and the Rate of the Convergence with P-Version by Using Finite Element Analysis

Abstract

The goal of this study is to further investigate and to develop a more effi cient way in the error estimate and the rate of the convergence for the adaptive mesh p-refi nement procedure in the fi nite element analysis for two-dimensional and threedimensional elastostatic mechanics problems. The oscillation of the stress fi eld around singularity points is also considered in the refi nement process. These oscillations will allow to determine the behaviors of the stress fi eld through the element boundary. The exact energy norm ||u_EX||_E of the structure can be estimated by a procedure called Richardson’s extrapolation. In this problem, we need to defi ne the three unknowns (||u_EX||_E(Ω))², k, and β which is difi cult and requires higher cost of computation in the energy norm. To overcome this problem, a modifi cation in the Richardson’s extrapolation is proposed. The solution obtain will be more accurate. If the numerical perturbation and the residual errors should be decreased. Specially, the computation cost in particular will be not expensive.