A general accuracy criterion for finite element approximation

The accuracy of Finite Element approximation depends on the size and shape of elements. The proposed theory clarifies the source of shape related errors. A new general accuracy condition based on the maximum eigenvalue of the element stiffness matrix (or, alternatively, its trace) is presented. Several new and several familiar geometric criteria follow directly from the eigenvalue condition as particular cases. The new accuracy criterion can be used in engineering practice as an a priori measure of the quality of finite element meshes.