On convergence of displacement finite elements, with an application to singularity problems

The formula for the truncation error in the energy product for conforming displacement finite elements is well known and a simple modification of this rule is proposed for noneonforming elements. It is also shown that two distinct types of error affect the convergence of the stress solutions, the second of which is usually neglected but is more significant and is 0(h 2) regardless of the order of the element interpolation. A clear knowledge of convergence behaviour then allows extrapolation of finite element solutions and this proves useful in the detection, identification and measurement of singularities.