On the enhanced strain finite element method for incompressible linear elasticity

In this paper we are concerned with the enhanced strain finite element method for nearly incompressible linear elasticity, in which enhanced strain space plays a key role. We propose a simple and unified way to define the enhanced strain space for k-order finite elements in both two and three dimensions. We show that the approximations generated by the enhanced strain finite element method with the new enhanced strain space possess the optimal error estimates. Moreover, we derive efficient preconditioners for the saddle-point system arising from this enhanced strain finite element method, such that the saddle-point system can be solved in a cheap manner. The numerical results show that our theoretical results are right, and the new method is very effective.