Energy-corrected finite element methods for the Stokes system

The solution of elliptic partial differential equations in a two-dimensional domain with re-entrant corners typically lacks full H²-regularity, and standard finite element approximations on uniformly refined meshes do not, in general, show optimal order convergence in suitably weighted L²-norms. Energy-corrected finite element techniques are based on a simple but parameter-dependent local modification of the stiffness matrix. If applied properly, optimal order convergence in weighted L²-norms can be recovered and the pollution effect is eliminated. Here, we generalize the ideas to the Stokes system and show that by using more than one correction parameter, optimal order convergence can be obtained.