Abstract

This study presents a mixed finite element formulation able to address nearly-incompressible problems explicitly. This formulation is applied to elements with independent and equal interpolation of displacements and strains, stabilized by variational subscales (VMS). As a continuation of the study presented in reference [23], in which the strains sub-scale was introduced, in this work the effects of sub-scale displacements are included, in order to stabilize the pressure field. The formulation avoids the Ladyzhenskaya-Babuska-Brezzi (LBB) condition and only requires the solution of a diagonal system of equations. The main aspects of implementation are also discussed. Finally, numerical examples validate the behaviour of these elements compared with the irreductible formulation.