Error Bounds for Exponentially Fitted Galerkin Methods Applied to Stiff Two-Point Boundary Value Problems

摘要

A linear second order singularly perturbed two point boundary-value problem is considered. Discretization by means of Petrov-Galerkin methods of finite element type, where the trial spaces contain piecewise exponentials, is studied. Error bounds, both pointwise and in the energy norm, are derived. The relation with other special difference schemes is shown and the error bounds obtained are compared with numerical results.