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

摘要

Stynes and O'Riordan, 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 h~(1/2) 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.