The inf-sup condition for the mapped \(Q_k-P_{k-1}^{\text{disc}}\) element in arbitrary space dimensions. (English) Zbl 1016.65073

Matthies, G.; Tobiska, L.

Computing 69, No. 2, 119-139 (2002).

The authors consider the numerical solution of the Stokes and Navier Stokes equations by means of finite elements. They discuss the use of the \(Q_k-P_{k-1}^{\text{disc}}\) element and the stability of the process when calculating the velocity and pressure fields of incompressible flow. No actual physical illustration of the ideas is given.

Reviewer: Ll.G.Chambers (Bangor)

MSC:

65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q30	Navier-Stokes equations
76M10	Finite element methods applied to problems in fluid mechanics
76D05	Navier-Stokes equations for incompressible viscous fluids

Keywords:

Babuška-Brezzi condition; Stokes problem; finite element method; Navier Stokes equations; stability; incompressible flow