A Galerkin/least-square finite element formulation for nearly incompressible elasticity/stokes flow

A Galerkin/least-square finite element formulation (GLS) is used to study mixed displacement-pressure formulation of nearly incompressible elasticity. In order to fully incorporate the effect of the residual-based stabilized term to the weak form, the second derivatives of shape functions were also derived and accounted, which can accurately discretize the residual term and improve the GLS method as well as the Petrov–Galerkin method. The numerical studies show that improved stabilized method can effectively remove volumetric locking problem for incompressible elasticity and stabilize the pressure field for stokes flow. When apply GLS to study material nonlinearity, the derivative of tangent modulus at the integration point will be required. Both advantage and disadvantage of using GLS method for nearly incompressible elasticity/stokes flow were demonstrated.