Uniform error estimates for an exponentially fitted finite element method for singularly perturbed elliptic equations

We consider a linear singularly perturbed elliptic equation on (0, 1) (2). In a recent paper [W. Dorfler, SIAM J. Numer. Anal., 36 (1999), pp. 1878-19 00] we proved uniform (in the perturbation parameter) estimates for solutio ns and an abstract a priori error estimate. Now we show, for some examples, that one can achieve uniform error estimates on a rectangular mesh using e xponentially fitted finite elements. These are constructed as tensor produc ts from solutions of local one-dimensional constant coefficient problems. E stimates are obtained in the L-2-norm and, assuming discrete stability, als o in the L-infinity-norm.