Mixed and nonconforming finite element methods for the Stokes problem. (English) Zbl 0846.35100
Summary: We analyze a family of mixed finite element methods for the Stokes problem. The mixed method considered is based on the use of the tensor gradient of the velocity as an auxiliary variable and Lagrange multipliers to impose interelement continuity. Error estimates of optimal order are derived. We further establish an equivalence between the family of mixed finite elements and certain modified versions of nonconforming finite element methods.
MSC:
35Q30 | Navier-Stokes equations |
76M10 | Finite element methods applied to problems in fluid mechanics |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |