@Article{EAJAM-15-314,
author = {Li , ZheSun , Tao and Yi , Lijun},
title = {Postprocessing-Based a Posteriori Error Estimation for Spectral Galerkin Approximations of Fourth-Order Boundary Value Problems},
journal = {East Asian Journal on Applied Mathematics},
year = {2025},
volume = {15},
number = {2},
pages = {314--343},
abstract = {<p style="text-align: justify;">A postprocessing-based a posteriori error estimates for the spectral Galerkin
approximation of one-dimensional fourth-order boundary value problems are developed. Our approach begins by introducing a novel postprocessing technique aimed at
enhancing the accuracy of the spectral Galerkin approximation. We prove that this post-processing step improves the convergence rate in both $L^2$- and $H^2$-norm. Using post-processed superconvergence results, we construct several a posteriori error estimators
and prove that they are asymptotically exact as the polynomial degree increases. We
further extend the postprocessing technique and error estimators to more general one-dimensional even-order equations and to multidimensional fourth-order equations. The
results of numerical experiments illustrate the efficiency of the error estimators.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.2023-268.120324},
url = {http://global-sci.org/intro/article_detail/eajam/23752.html}
}