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Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations. (English) Zbl 0637.76024
The Lagrange-Galerkin method is a numerical technique for solving convection-dominated diffusion problems, based on combining a special discretization of the Lagrangian material derivative along particle trajectories with the Galerkin finite element method. In this paper optimal error estimates are presented for the Lagrange-Galerkin mixed finite element approximation of the Navier-Stokes equations in a velocity/pressure formulation. The method is shown to be nonlinearly stable.
Reviewer: E.Süli
MSC:
76D05Navier-Stokes equations (fluid dynamics)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
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