A stabilized mixed finite element method based on g-biorthogonal systems for nearly incompressible elasticity

We present a finite element method for nearly incompressible elasticity using a mixed formulation of linear elasticity in the displacement–pressure form. The idea of stabilization of an equal order interpolation for Stokes equations is combined with biorthogonality to get rid of the bubble functions. A Petrov–Galerkin formulation for the pressure equation is used, where the trial and test spaces are different and form a g-biorthogonal system. This novel approach leads to a displacement-based low order finite element method for nearly incompressible elasticity for simplicial, quadrilateral and hexahedral meshes. Numerical results are provided to demonstrate the efficiency of the approach.