Numerical Analysis of a Second Order Pure Lagrange-Galerkin Method for Convection-Diffusion Problems. Part II: Fully Discretized Scheme and Numerical Results

We analyze a second order pure Lagrange-Galerkin method for variable coefficient convection-(possibly degenerate) diffusion equations with mixed Dirichlet-Robin boundary conditions. In a previous paper the proposed second order pure Lagrangian time discretization scheme has been introduced and analyzed for the same problem. Moreover, the l(H) stability and l(H) error estimates of order O(∆t) has been obtained. In the present paper l(H) error estimates of order O(∆t) + O(h) 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.