Section: New Results

Stabilized finite element methods: discontinous Galerkin

Participants : Roland Becker, Daniela Capatina, Julie Joie, Nour Seloula.

We have developed a new discontinuous Galerkin scheme for the Stokes equations and corresponding three-field equations. In this work, which is part of the Phd Thesis of Julie Joie, we introduce a modification of the stabilization term in the standard DG-IP method. This allows for a cheaper implementation and has a more robust behavior with respect to the stabilization parameter; we have shown convergence towards the solution of non-conforming finite element methods for linear, quadratic and cubic polynomial degrees. This scheme has been extended to the three-field formulation of the Stokes problem, which is a further step towards the polymer project of Section  4.2 . Since it is well known that the non-conforming finite element approximations do not verify the discrete Korn inequality, an appropriate further stabilization term is introduced. We have analyzed different techniques to do so. Our results have been presented in [31] , [22] . The methods have been implemented in the activities of Section  5.4 and are available for testing.