TY - JOUR
T1 - Postprocessing-Based a Posteriori Error Estimation for Spectral Galerkin Approximations of Fourth-Order Boundary Value Problems
AU - Li , Zhe
AU - Sun , Tao
AU - Yi , Lijun
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 314
EP - 343
PY - 2025
DA - 2025/01
SN - 15
DO - http://doi.org/10.4208/eajam.2023-268.120324
UR - https://global-sci.org/intro/article_detail/eajam/23752.html
KW - Spectral Galerkin method, fourth-order boundary value problem, superconvergent post-processing, a posteriori error estimation.
AB - <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>