Stability analysis for Eulerian and semi-Lagrangian finite-element formulation of the advection-diffusion equation (Q1963089)

The stability of the finite element approximation to the linearized two-dimensional advection-diffusion equation is studied. Bilinear basis functions on rectangular elements are considered. The paper analytically compares a semi-implicit Eulerian method with a semi-implicit semi-Lagrangian method. It is shown that for small or no diffusion the semi-implicit semi-Lagrangian method exhibits better amplitude, dispersion and group velocity errors. In the case when the diffusion coefficients are large, the semi-Lagrangian method loses its competitiveness.