A rational function approximation for the integration point in exponentially weighted finite element methods

Abstract

SUMMARYA rational function is presented for approximating the functionf(2) = coth t -l/z that appears in several exponentially fitted or weighted finite difference and finite element methods for convection-diffusion problems. The approximation is less expensive to evaluate than f ( z ) and provides greater accuracy than the doubly asymptotic approximation when z = O(1).