Asymptotic finite element method for boundary value problems

Abstract

Abstract The Asymptotic Finite Element method for improvement of standard finite element solutions of perturbation equations by the addition of asymptotic corrections to the right hand side terms is presented. It is applied here to 1‐D and 2‐D diffusion–convection equations and to non‐linear similarity equations. Excellent results were obtained without the a priori use of special trial and test functions. Theoretical expectations were confirmed.