On the finite element approximation of the nonstationary Navier-Stokes problem
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In this note we report some basic convergence results for the semi-discrete finite element Galerkin approximation of the nonstationary Navier-Stokes problem. Asymptotic error estimates are established for a wide class of so-called conforming and nonconforming elements as described in the literature for modelling incompressible flows. Since the proofs are lengthy and very technical the present contribution concentrates on a precise statement of the results and only gives some of the key ideas of the argument for proving them. Complete proofs for the case of conforming finite elements may be found in a joint paper of J. Heywood, R. Rautmann and the author , whereas the nonconforming case will be treated in detail elsewhere.
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- Crouxeiz, M.; Raviart, P.-A.: Conforming and nonconforming finite element methods for solving the stationary Stokes equation I. R.A.I.R.O. Anal. Numer. 3 (1973), 33–76.Google Scholar
- Fortin, M.: Résolution des équations des fluides incompressibles par la méthode des éléments finis. In Proceedings of the Third International Conference on the Numerical Methods in Fluid Mechanics, Springer: Berlin-Heidelberg-New York 1972.Google Scholar
- Heywood, J.G.: Classical solutions of the Navier-Stokes equations. In this Proceedings.Google Scholar
- Heywood, J.G.; Rannacher, R.; Rautmann, R.: Semidiscrete finite element Galerkin approximation of the nonstationary Navier-Stokes problem. To appear.Google Scholar
- Jamet, P.,; Raviart, P.-A.: Numerical solution of the stationary Navier-Stokes equation by finite element methods. In Computing Methods in Applied Sciences and Engineering, Part 1, Lecture Notes in Computer Sciences, Vol. 10, Springer: Berlin-Heidelberg-New York 1974.Google Scholar
- Rautmann, R.: On the convergence-rate of nonstationary Navier-Stokes approximations. In this Proceedings.Google Scholar