We prove a priori optimal-order error estimates in a weighted energy norm for several Eulerian–Lagrangian methods for singularly perturbed, time-dependent convection-diffusion equations with full regularity. The estimates depend only on certain Sobolev norms of the initial and right-hand side data, but not on ε or any norm of the true solution, and so hold uniformly with respect to ε. We use the interpolation of spaces and stability estimates to derive an ε-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.
Published in Siam Journal of Numerical Analysis, Volume 45, Issue 3, 2007, pages 1305-1329.
© Siam Journal of Numerical Analysis 2007, Society for Industrial and Applied Mathematics
Wang, H., & Wang, K. (2007). Uniform Estimates for Eulerian–Lagrangian Methods for Singularly Perturbed Time-Dependent Problems. SIAM Journal On Numerical Analysis, 45(3), 1305-1329. doi: 10.1137/060652816