Error in the upwind differencing of the convection-diffusion equation
The authors consider the linear convection-diffusion equation for steady- state problems with Dirichlet boundary conditions in one and two dimensions. The boundary value problem is approximated by first-order upwind difference schemes on a locally refined mesh. Error estimates are given. The existence of an asymptotic expansion for the discretization error is established. A difference correction procedure is described. Three numerical examples are given to prove the validity of the presented results.
scientific article; zbMATH DE number 804737
scientific article