An Optimal-Order Error Estimate for an ELLAM Scheme for Two-Dimensional Linear Advection-Diffusion Equations

Abstract

An Eulerian--Lagrangian localized adjoint method (ELLAM) is presented and analyzed for two-dimensional linear advection-diffusion partial differential equations (PDEs). An optimal-order error estimate in the L2 norm and a superconvergence estimate in a discrete H1 norm are derived. Numerical experiments are performed to verify the theoretical estimates.