Solving convection-dominated anisotropic diffusion equations by an exponentially fitted finite volume method

This paper deals with the numerical solution by an exponentially fitted finite volume method of a linear convection-dominated diffusion equation with a constant matrix diffusion coefficient and a singular perturbation parameter . The equation is first transformed into one with a scalar diffusion coefficient by a simple coordinate transformation, and an exponentially fitted finite volume method is then applied to the resulting equation. Application of this approach to the time-space discretisation of time-dependent singularly perturbed convection-diffusion equations is also discussed. Numerical examples are solved to demonstrate the usefulness of this approach. The numerical results show that the method is efficient and stable for a large range of values of .