Numerical analysis of a second order pure lagrange-galerkin method for convection-diffusion problems. Part II: Fully Discretized scheme and numerical results

摘要

We analyze a second order pure Lagrange-Galerkin method for variable coefficient convection-diffusion (possibly degenerate-diffusion) equations with mixed Dirichlet-Robin boundary conditions. In a previous paper the proposed second order pure Lagrangian time discretization scheme was introduced and analyzed for the same problem. More precisely, the l∞(H~1) stability and l∞(H~1) error estimates of order O(Δt ~2) had been obtained. Moreover, for the particular case of incompressible flows, stability inequalities with constants independent of the final time have been stated. In the present paper l∞(H~1) error estimates of order O(Δt~2) + O(h~k) are obtained for the fully discretized pure Lagrange-Galerkin method. To prove these results we use some properties obtained in the previous paper. Finally, numerical tests are presented that confirm the theoretical results.