Nearly Incompressible Linear Elasticity Using Simplicial Meshes

We present two finite element methods for simplicial meshes to approximate the solution of the problem of nearly incompressible elasticity. Although both approaches are based on mixed formulations of linear elastic equations and biorthogonal systems, one of them is nonsymmetric, and the other symmetric. An interesting feature of both approaches is that displacement-based formulations can be obtained by statically condensing out all other auxiliary variables from the system. These approaches lead to displacement-based low order finite element methods for nearly incompressible elasticity using simplicial meshes. Uniform convergence of finite element approximations in the incompressible limit is proved. Numerical results are provided to demonstrate the efficiency of the approach. ∗E-mail address: [email protected] 2 Bishnu P. Lamichhane