'Society for Industrial & Applied Mathematics (SIAM)'
Doi
Abstract
A postprocessing technique, developed earlier for spectral methods, is extended
here to Galerkin nite-element methods for dissipative evolution partial di erential equations. The
postprocessing amounts to solving a linear elliptic problem on a ner grid (or higher-order space)
once the time integration on the coarser mesh is completed. This technique increases the convergence
rate of the nite-element method to which it is applied, and this is done at almost no additional
computational cost. The numerical experiments presented here show that the resulting postprocessed
method is computationally more e cient than the method to which it is applied (say, quadratic nite
elements) as well as standard methods of similar order of convergence as the postprocessed one (say,
cubic nite elements). The error analysis of the new method is performed in L2 and in L1 norms.DGICYT PB95-21