A finite element method for the stationary Stokes equations using trial functions which do not have to satisfy 𝑑𝑖𝑣𝜈=0

Falk, Richard S.

doi:10.1090/S0025-5718-1976-0421109-7

A finite element method for the stationary Stokes equations using trial functions which do not have to satisfy $\textrm {div}\nu =0$
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Math. Comp. 30 (1976), 698-702 Request permission

Abstract:

By adding a term to the variational equations, we derive a new finite element method for the stationary Stokes equations which eliminates the ${\operatorname {div}}\upsilon = 0$ restriction on the trial functions. The method is described using continuous piecewise linear functions, and the optimal $O(h)$ order of convergence estimate is derived for the error in the ${H^1}(\Omega )$ norm.

References

M. Crouzeix and P.-A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 7 (1973), no. R-3, 33–75. MR 343661
Richard S. Falk, An analysis of the finite element method using Lagrange multipliers for the stationary Stokes equations, Math. Comput. 30 (1976), no. 134, 241–249. MR 0403260, DOI 10.1090/S0025-5718-1976-0403260-0

Advances in Computer Methods for Partial Differential Equations

Richard S. Falk and J. Thomas King, A penalty and extrapolation method for the stationary Stokes equations, SIAM J. Numer. Anal. 13 (1976), no. 5, 814–829. MR 471382, DOI 10.1137/0713064
P. Jamet and P.-A. Raviart, Numerical solution of the stationary Navier-Stokes equations by finite element methods, Computing methods in applied sciences and engineering (Proc. Internat. Sympos., Versailles, 1973) Lecture Notes in Comput. Sci., Vol. 10, Springer, Berlin, 1974, pp. 193–223. MR 0448951

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