The Mac Scheme and Related Finite Element Method for Nearly Incompressible Elasticity

The marker and cell (MAC) scheme is formulated for the planar linear elasticity problem in which the two components of the displacement and the pressure are defined on different meshes. The optimal rate error estimates that are uniformly valid, independent of the value of the Lamé constant λ ∈ (0, +∞), are obtained for both the displacement and the pressure. Furthermore, we get the results of related mixed finite element method, similar to the MAC, without exhibiting the degeneracy phenomenon. Some numerical examples for the MAC scheme and related FEM are presented