We present an Eulerian-Lagrangian localized adjoint method (ELLAM) scheme for initial-boundary value problems for advection-reaction partial differential equations in multiple space dimensions. The derived numerical scheme is not subject to the Courant-Friedrichs-Lewy condition and generates accurate numerical solutions even if large time steps are used. Moreover, the scheme naturally incorporates boundary conditions into its formulation without any artificial outflow boundary conditions needed, and it conserves mass. An optimal-order error estimate is proved for the scheme. Numerical experiments are performed to verify the theoretical estimate.
Published in Siam Journal of Numerical Analysis, Volume 38, Issue 6, 2001, pages 1846-1885.
© SIAM Journal On Numerical Analysis 2001, Society for Industrial and Applied Mathematics
Wang, H., Shi, X., & Ewing, R. (2001). An ELLAM Scheme for Multidimensional Advection-Reaction Equations and Its Optimal-Order Error Estimate. SIAM Journal On Numerical Analysis, 38(6), 1846-1885. doi: 10.1137/s0036142999362389