Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations

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.