  In this paper, we propose and analyze an abstract stabilized mixed finite
element framework that can be applied to nonlinear incompressible elasticity
problems. In the abstract stabilized framework, we prove that any mixed finite
element method that satisfies the discrete inf-sup condition can be modified so
that it is stable and optimal convergent as long as the mixed continuous
problem is stable. Furthermore, we apply the abstract stabilized framework to
nonlinear incompressible elasticity problems and present numerical experiments
to verify the theoretical results.
