An unusual stabilized finite element method for a generalized Stokes problem. (English) Zbl 1019.65087
Authors’ summary: An unusual stabilized finite element is presented and analyzed herein for a generalized Stokes problem with a dominating zeroth order term. The method consists in subtracting a mesh dependent term from the formulation without compromising consistency. The design of this mesh dependent term, as well as the stabilization parameter involved, are suggested by bubble condensation. Stability is proven for any combination of velocity and pressure spaces, under the hypotheses of continuity for the pressure space. Optimal order error estimates are derived for the velocity and the pressure, using the standard norms for these unknowns. Numerical experiments confirming these theoretical results, and comparisons with previous methods are presented.
Reviewer: Dinh Nho Hao (Brussel)
MSC:
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
35Q30 | Navier-Stokes equations |
65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
76M10 | Finite element methods applied to problems in fluid mechanics |
76D07 | Stokes and related (Oseen, etc.) flows |