Postprocessing-Based a Posteriori Error Estimation for Spectral Galerkin Approximations of Fourth-Order Boundary Value Problems
Year: 2025
Author: Zhe Li, Tao Sun, Lijun Yi
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 2 : pp. 314–343
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2023-268.120324
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 2 : pp. 314–343
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Spectral Galerkin method fourth-order boundary value problem superconvergent post-processing a posteriori error estimation.