element edges (cf., for example, [4]), or a tensor product of the one dimensional approximations along element edges
In this paper we develop an exponentially fitted finite element method for a singularly perturbed advection-diffusion problem with parallel to coordinate axes (cf., for example, [6]). The cona singular perturbation parameter . This finite element method struction of genuine piecewise exponential basis functions is based on a set of novel piecewise exponential basis functions on triangular meshes has been sought, but still remains an constructed on unstructured triangular meshes. The basis functions open problem except for some special cases (cf., for examcan not be expressed explicitly, but the values of each of them and ple [7]). Another progress on this is the divergence free its associated flux at a point are determined by a set of two-point boundary value problems which can be solved exactly. A method shape functions for the semiconductor device equations for evaluating elements of the stiffness matrix is also proposed for proposed recently by Sacco, Gatti, and Gotusso (cf. [9]).
the case that is small. Numerical results, presented to validate
In this paper we present an exponentially fitted Galerkin the method, show that the method is stable for a large range of .
finite element method based on a novel set of piecewise
It is also shown by the numerical results that the rate of convergence of the method in an energy norm is of order h 1/2 when is exponential basis functions constructed on an unstructured small. ᮊ 1997 Academic Press triangular mesh. At each point x in a solution domain, the finite element subspace spanned by these basis functions yields constant approximations to the flux projections onto
2. THE PROBLEM methods for singularly perturbed advection-diffusion
Consider stationary, linear, advection-diffusion probequations in higher dimensions are essentially based on a one-dimensional constant approximation to the flux along lems of the form 253