Element by element <i>a posteriori</i> error estimation and improvement of stress solutions for two‐dimensional elastic problems

Abstract

Abstract A quantitative method of a posteriori error estimation based on finite element solutions is developed. The proposed method can estimate the error of solutions obtained by the finite element method for two‐dimensional elastic problems with 4‐node elements. Since the error is estimated element by element, the proposed method does not require a large memory or long computing time. Not only rectangular elements but also arbitrarily shaped 4‐node elements can be used in this method for estimating the error in the finite element computation with high accuracy. The finite element solutions are improved by adding the estimated errors onto the original solutions. The proposed method can be utilized for any type of linear problem if an isoparametric finite element method is used.