A Subgrid Viscosity Lagrange-Galerkin Method for Convection-Diffusion Problems

Abstract

We present and analyze a subgrid viscosity Lagrange-Galerkin method that combines the subgrid eddy viscosity method proposed in W. Layton, A connection between subgrid scale eddy viscosity and mixed methods. Appl. Math. Comp., 133: 147-157, 2002, and a conventional Lagrange-Galerkin method in the framework of $P_1\oplus$ cubic bubble finite elements. This results in an efficient and easy to implement stabilized method for convection dominated convection-diffusion-reaction problems. Numerical experiments support the numerical analysis results and show that the new method is more accurate than the conventional Lagrange-Galerkin one.