An ELLAM scheme for multidimensional advection-reaction equations and its optimal-order error estimate

We present an Eulerian Lagrangian localized adjoint method (ELLAM) scheme f or initial-boundary value problems for advection-reaction partial different ial equations in multiple space dimensions. The derived numerical scheme is not subject to the Courant-Friedrichs-Lewy condition and generates accurat e numerical solutions even if large time steps are used. Moreover, the sche me naturally incorporates boundary conditions into its formulation without any artificial out ow boundary conditions needed, and it conserves mass. An optimal-order error estimate is proved for the scheme. Numerical experimen ts are performed to verify the theoretical estimate.