Compatibility condition and existence results in discrete finite incompressible elasticity

Abstract A theory on the existence of solutions of the discretized equilibrium equations in incompressible finite elasticity is given. A compatibility condition between the space of displacements and the space of pressures is introduced and is studied in a particular case of finite element spaces, using Q 1 and Q 0 isoparametric elements. An original assembling of these elements is presented which leads to discrete spaces satisfying the compatibility condition.