NUMERICAL ANALYSIS OF A SECOND ORDER PURE LAGRANGE-GALERKIN METHOD FOR CONVECTION-DIFFUSION PROBLEMS. PART II: FULLY DISCRETIZED SCHEME AND NUMERICAL RESULTS

作者：Benitez Marta^*; Bermudez Alfredo

来源：SIAM Journal on Numerical Analysis, 2012, 50(6): 2824-2844.

DOI：10.1137/100809994

• convection-diffusion equation
• Lagrangian method
• characteristics method
• Galerkin discretization
• stability
• error estimates
• second order schemes

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(infinity)(H-1) stability and l(infinity)(H-1) error estimates of order O(Delta t(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(infinity)(H-1) error estimates of order O(Delta t(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.

• 出版日期2012