Finite element analysis of exponentially fitted Lumped schemes for time-dependent convection-diffusion problems

Abstract

In the paper we consider a singularly perturbed linear parabolic initialboundary value problem in one space variable. Two exponential fitted schemes are derived for the problem using Petrov-Galerkin finite element methods with various choices of trial and test spaces. On rectangular meshes which are either arbitrary or slightly restricted, we derive global energy norm andL 2 norm and localL ? error bounds which are uniform in the diffusion parameter. Numerical results are also persented.