Investigation of a Posteriori Error Analysis for Plane Stress Problems by the Finite Element Method and Updating Stresses

Abstract

The estimation of the discretisation error in the finite element method is considered in this paper. The proposed method can estimate solution errors obtained by the finite element method for 2-dimensional elastic problems with 4-node elements. Because the quadratic term is expected to dominate the error field, an 8-node element is utilised in the estimation. Since error is estimated element by element, this does not lead to excessive computer memory or processing time usage. Not only rectangular elements but also any shape 4-node elements can be used for highly accurate error estimation in finite element computation. An error norm is computed in the paper which can indicate a relative error in the elements. The finite element solutions are also considerably improved by adding the estimated errors onto the original solutions. The proposed method can be utilised for any type of linear problem if an isoparametric finite element method is used.