A stable enriched Galerkin element for the Stokes problem

作者：Chaabane Nabil; Girault Vivette; Riviere Beatrice^*; Thompson Travis

来源：Applied Numerical Mathematics, 2018, 132: 1-21.

DOI：10.1016/j.apnum.2018.04.008

• inf-sup condition
• Enriched Galerkin
• Stabilized divergence operator
• Fortin's Lemma
• Local mass conservation
• Error estimates

We propose a stable element for the divergence operator that approximates the velocity by continuous linear polynomials plus piecewise constants and the pressure by piecewise constants. A uniform inf-sup condition is obtained for conforming meshes in two or three dimensions. The resulting method belongs to the class of enriched Galerkin methods, and is applied to the solution of a Stokes system. A priori error estimates in the energy norm and in the L-2 norm are derived. Extensions to the Navier-Stokes system are presented.

• 出版日期2018-10