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

Author:
Richard S. Falk

Journal:
Math. Comp. **30** (1976), 698-702

MSC:
Primary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1976-0421109-7

MathSciNet review:
0421109

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Abstract: By adding a term to the variational equations, we derive a new finite element method for the stationary Stokes equations which eliminates the restriction on the trial functions. The method is described using continuous piecewise linear functions, and the optimal order of convergence estimate is derived for the error in the norm.

**[1]**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**0343661****[2]**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**, https://doi.org/10.1090/S0025-5718-1976-0403260-0**[3]**R. S. FALK, "An analysis of the penalty method and extrapolation for the stationary Stokes equations,"*Advances in Computer Methods for Partial Differential Equations*, R. Vichnevetsky (Editor), Proc. AICA Sympos., Lehigh Univ., June 1975, pp. 66-69.**[4]**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**0471382**, https://doi.org/10.1137/0713064**[5]**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) Springer, Berlin, 1974, pp. 193–223. Lecture Notes in Comput. Sci., Vol. 10. MR**0448951****[6]**B. KELLOGG & J. OSBORN,*A Regularity Result for the Stokes Problem in a Convex Polygon*, Technical Note BN-804, Institute for Fluid Dynamics and Applied Mathematics, Univ. of Maryland, 1974.**[7]**R. TEMAM,*On the Theory and Numerical Analysis of the Navier-Stokes Equations*, Lecture Note # 9, Univ. of Maryland, June 1973.

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DOI:
https://doi.org/10.1090/S0025-5718-1976-0421109-7

Article copyright:
© Copyright 1976
American Mathematical Society