Abstract
Mixed finite element method has been successfully applied to the analysis of incompressible solid and fluid, shell and beam structures and electromagnetic fields, etc. However it is well known that mixed finite element method may work well in the solution of certain problems but perform very poorly on other problems. In this paper, first, a brief review of the stability conditions for mixed variational principle, which is known as the LBB condition, is given. Then a numerical prediction procedure for the discrete LBB condition which has recently been developed by Malkus (Int. J. Eng. Sci., 19 (1981), 1299) and Chapelle et al. (Compt. & Struct., 47 (1993), 537) is described. Finally the performances of two-and three-dimensional incompressible mixed elements, such as quadrilateral, triangular, hexahedral and tetrahedral elements are systematically investigated based on the discrete LBB condition.
