Finite difference approximations of multidimensional unsteady convectiondiffusionreaction equations
In this paper, the numerical approximation of unsteady convectiondiffusionreaction equations with finite difference method on a special grid is studied in the convection or reaction-dominated regime. We extend the method [19] which was designed for multidimensional steady convectiondiffusionreaction equations to unsteady problems. We investigate two possible different ways of combining the discretization in time and in space (where the sequence of the discretizations is interchanged). Discretization in time is performed by using CrankNicolson and Backward-Euler finite difference schemes, while for the space discretization we consider the method [19]. Numerical tests are presented to show good performance of the method.
unsteady convectiondiffusionreaction finite difference method finite element method