On Convergence of the Exponentially Fitted Finite Volume Method with an Anisotropic Mesh Refinement for a Singularly Perturbed Convection-Diffusion Equation

This paper presents a convergence analysis for the exponentially fitted finite volume method in two dimensions applied to a linear singularly perturbed convection-diffusion equation with exponential boundary layers. The method is formulated as a nonconforming Petrov-Galerkin finite element method with an exponentially fitted trial space and a piecewise constant test space. The corresponding bilinear form is proved to be coercive with respect to a discrete energy norm. It is also shown that the approximation error in the discrete energy norm is bounded above by C(h ½ +h√|lnε/lnh|) with C independent of the mesh parameter h,, the diffusion coefficient ε, and the exact solution of the problem. Numerical results are presented to verify the theoretical rates of convergence.