Summary
The Lagrange-Galerkin method is a numerical technique for solving convection — dominated diffusion problems, based on combining a special discretisation of the Lagrangian material derivative along particle trajectories with a Galerkin finite element method. We present optimal error estimates 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.
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Süli, E. Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations. Numer. Math. 53, 459–483 (1988). https://doi.org/10.1007/BF01396329
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DOI: https://doi.org/10.1007/BF01396329