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Full-Text Articles in Physical Sciences and Mathematics
An Ellam Scheme For Multidimensional Advection-Reaction Equations And Its Optimal-Order Error Estimate, Hong Wang, Xiquan Shi, Richard E. Ewing
An Ellam Scheme For Multidimensional Advection-Reaction Equations And Its Optimal-Order Error Estimate, Hong Wang, Xiquan Shi, Richard E. Ewing
Faculty Publications
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.