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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. Numerical results are presented to verify the theoretical rates of convergence.

computational methods in applied mathematics

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