THREE-DIMENSIONAL FINITE ELEMENT METHODS FOR THE STOKES PROBLEM

The tetrahedral finite element approximation of the Stokes problem is analyzed by means of polynomials piecewise of degree k + 1 for the velocity and continuous piecewise of degree k for the pressure. A stability result is given for every k ≥ 1.

[1]  Rolf Stenberg,et al.  On some three-dimensional finite elements for incompressible media , 1987 .

[2]  F. Brezzi On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers , 1974 .

[3]  F. Brezzi,et al.  On the Stabilization of Finite Element Approximations of the Stokes Equations , 1984 .

[4]  Daniele Boffi,et al.  MINIMAL STABILIZATIONS OF THE Pk+1-Pk APPROXIMATION OF THE STATIONARY STOKES EQUATIONS , 1995 .

[5]  I. Babuska The finite element method with Lagrangian multipliers , 1973 .

[6]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[7]  F. Brezzi,et al.  Stability of higher-order Hood-Taylor methods , 1991 .

[8]  Rüdiger Verfürth,et al.  Error estimates for a mixed finite element approximation of the Stokes equations , 1984 .

[9]  L. R. Scott,et al.  Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials , 1985 .

[10]  Daniele Boffi,et al.  STABILITY OF HIGHER ORDER TRIANGULAR HOOD-TAYLOR METHODS FOR THE STATIONARY STOKES EQUATIONS , 1994 .

[11]  O. Pironneau,et al.  Error estimates for finite element method solution of the Stokes problem in the primitive variables , 1979 .

[12]  Vivette Girault,et al.  Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms , 1986, Springer Series in Computational Mathematics.

[13]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[14]  P. Hood,et al.  A numerical solution of the Navier-Stokes equations using the finite element technique , 1973 .