On the Application of Extrapolation, Deferred Correction and Defect Correction to Discrete-time Galerkin Methods for Parabolic Problems

Conditions which ensure the applicability of extrapolation-in-timeof the backward-difference Galerkin and Crank—NicolsonGalerkin methods for linear parabolic initial-boundary problemsare discussed. Deferred correction and defect correction proceduresfor these discrete-time Galerkin methods are formulated andtheir theoretical properties summarized. These procedures yieldapproximations which are up to fourth-order correct in time,and whose computation requires less work per time step thanthat required by extrapolation. The results of numerical experiments,which demonstrate the expected rates of convergence with respectto the time discretization of the various techniques, are presented. ^*The work of this author was supported in part by the NationalScience Foundation under grant MCS-8102295