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Zbl 0637.76024
Süli, Endre
Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations. (English)
[J] Numer. Math. 53, No.4, 459-483 (1988). ISSN 0029-599X; ISSN 0945-3245/e

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.
[E.Süli]

MSC 2000:: *76D05 Navier-Stokes equations (fluid dynamics)
65N30 Finite numerical methods (BVP of PDE)

Keywords: Lagrange-Galerkin method; convection-dominated diffusion problems; special discretisation; Lagrangian material derivative; particle trajectories; Galerkin finite element method; optimal error estimates; Lagrange-Galerkin mixed finite element approximation; Navier-Stokes equations; velocity/pressure formulation

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