On a general decomposition of the error of an approximate stress field in elasticity - Debongnie, Jean-François; Beckers, Pierre (Computer Assisted Methods in Engineering and Science, 2023)
The errors of finite element approximations are analysed in a general frame, which is completely independent from the way through which the approximate solution was obtained. It is found that the error always admits decomposition in two terms, namely the equilibrium error and the compatibility error, which are orthogonal. Each of these admits upper and lower bounds that can be computed in a post-processing scheme.