(untitled) (Journal of Computational Mathematics, 1999)
In [16], Stynes and O'Riordan(91) introduced a local exponentially fitted finite element (FE) scheme for a singularly perturbed two-point boundary value problem without turning-point. An ε-uniform h^1/2-order accuracy was obtain for the ε-weighted energy norm. And this uniform order is known as an optimal one for global exponentially fitted FE schemes (see [6, 7, 12]). In present paper, this scheme is used to a parabolic singularly perturbed problem. After some subtle analysis, a uniformly in ε convergent order h|ln h|^1/2+ τ is achieved (h is the space step and τ is the time step), which sharpens the results in present literature. Furthermore, it implies that the accuracy order in [16] is actually h|ln h|^1/2 rather than h^1/2.