UNIFORM ESTIMATES OF AN EULERIAN-LAGRANGIAN METHOD FOR TIME-DEPENDENT CONVECTION-DIFFUSION EQUATIONS IN MULTIPLE SPACE DIMENSIONS

We prove a priori error estimates for a family of Eulerian-Lagrangian methods for time-dependent convection-diffusion equations in multiple space dimensions, which hold uniformly with respect to the vanishing parameter e. We use the interpolation of spaces and stability estimates to derive an e-uniform estimate for problems with minimal or intermediate regularity, where the convergence rates are proportional to certain Besov norms of the initial and right-hand side data. These estimates theoretically justify the strength of Eulerian-Lagrangian methods.