Pure equilibrium tetrahedral finite elements for global error estimation by dual analysis

This study presents a general porocedure of creating pure equilibrium tetrahedral finite elements. These elements are of the Fraeijs de Veubeke type. The spurious kinematical modes which inevitably appear in this approach are eliminated by converting each tetrahedron in a super-element consisting of four tetrahedral primitive elements. A mathematical discussion on the number of spurious kinematical modes is presented. The development of first and second degree elements is presented in detail, and their efficiency in the frame of global errror estimation by dual analysis is emphasized by two numerical applications. The main attribute of the error estimation by dual analysis is that it provides an upper bound of the discretization error.