TY - JOUR T1 - Finite Element Analysis of a Local Exponentially Fitted Scheme for Time-Dependent Convection-Diffusion Problems AU - Yue , Xing-Ye AU - Jiang , Li-Shang AU - Shih , Tsi-Min JO - Journal of Computational Mathematics VL - 3 SP - 225 EP - 232 PY - 1999 DA - 1999/06 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9097.html KW - Singularly perturbed, Exponentially fitted, Uniformly in $ε$ convergence, Petrov-Galerkin finite element method. AB -

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 $h|{\rm ln} h|^{1/2}+ τ$ 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 $h|{\rm ln} h|^{1/2}$ rather than $h^{1/2}$.