Local exponentially fitted finite element schemes for singularly perturbed convection–diffusion problems

Stynes and OʹRiordan, Math. Comp. 56 (1991) 663–675 considered a local exponentially fitted finite element (FE) scheme for a singular perturbed two-point boundary value problem, and gave an ε-uniform error estimate of h1/2 order in the energy norm. In the present paper, we will first prove that this scheme actually possesses an ε-uniform convergence order h|ln h|1/2 in the energy norm, then consider two other higher-order schemes.