A postprocess based improvement of the spectral element method

We present an approximate inertial manifold based postprocess to enhance th e accuracy of the spectral element method for evolutionary equations of dis sipative type. The analysis shows that the postprocess improves the order o f convergence. The postprocess consists on the resolution of a discrete ell iptic problem only once when the time evolution has been completed. The ove rcost is then negligible and the resulting postprocessed method is really a n improvement over the standard spectral element discretization to which is applied. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights res erved.