Sharp maximum norm error estimates for finite element approximations of the Stokes problem in 2-D

Etude des approximations a elements finis des equations de Stokes dans un domaine borne a l'aide d'une formulation mixte vitesse-pression. Etablissement d'estimations d'erreur quasi-optimales dans la norme maximum pour la vitesse, son gradient et les champs de pression

[1]  T. Dupont,et al.  Polynomial approximation of functions in Sobolev spaces , 1980 .

[2]  S. Agmon,et al.  Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I , 1959 .

[3]  Rolf Rannacher,et al.  Finite element methods for nonlinear elliptic systems of second order , 1980 .

[4]  Rolf Rannacher,et al.  Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations , 1982 .

[5]  C. Bernardi,et al.  Analysis of some finite elements for the Stokes problem , 1985 .

[6]  J. Nitsche,et al.  L∞-convergence of finite element approximations , 1977 .

[7]  Lamberto Cattabriga,et al.  Su un problema al contorno relativo al sistema di equazioni di Stokes , 1961 .

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

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

[10]  R. S. Falk,et al.  Error estimates for mixed methods , 1980 .

[11]  R. Kellogg,et al.  A regularity result for the Stokes problem in a convex polygon , 1976 .

[12]  Michel Fortin,et al.  An analysis of the convergence of mixed finite element methods , 1977 .

[13]  M. Fortin,et al.  A stable finite element for the stokes equations , 1984 .

[14]  P. Raviart,et al.  Conforming and nonconforming finite element methods for solving the stationary Stokes equations I , 1973 .

[15]  R. Scholz.  OptimalL∞-estimates for a mixed finite element method for second order elliptic and parabolic problems , 1983 .

[16]  Frank Natterer,et al.  Über die punktweise Konvergenz Finiter Elemente , 1975 .

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

[18]  R. Temam.  Navier-Stokes Equations , 1977 .