Section: New Results

Discontinous finite element methods

Participants : Roland Becker, Daniela Capatina, Julie Joie.

We have developed a new discontinuous Galerkin scheme for the Stokes equations and corresponding three-fields formulation. 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, see  [42] .