An anisotropic GLS-stabilized finite element method for incompressible flow problems

We consider a stabilized, finite element approximation of incompressible flow problems in primitive velocity–pressure variables, which is based on a GLS formulation. Equal order interpolation for the velocity and the pressure can be employed with this formulation. The method introduced here is specially developed to be used on anisotropic finite element meshes with large element aspect ratios. Rather than using a single stabilization parameter within each element, the Jacobian matrix of the affine transformation from the reference element is employed for stabilization purposes. Stability and anisotropic error estimates in a suitable mesh-dependent norm are proved for the linear Stokes problem. Numerical results confirm the accuracy and robustness of the proposed method compared to similar previous stabilized schemes.