A GENERAL ACCURACY CRITERION FOR FINITE-ELEMENT APPROXIMATION

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