Error Estimates for the Approximate Solution of Linear Fixed Point Equations

Abstract

The defects which are caused by the solutions of approximate equations in the original equation provide an effective tool for the asymptotically exact estimation of approximation errors. Using these defects may be justified without uniformity restrictions on the underlying mesh sequences. As an example, asymptotically exact error estimates are investigated for the numerical solution of a one‐dimensional linear diffusion‐convection equation by means of finite elements.