Postprocessing-Based a Posteriori Error Estimation for Spectral Galerkin Approximations of Fourth-Order Boundary Value Problems
Year: 2024
Type: article
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.
Authors: Zhe Li, Tao Sun, Lijun Yi
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4404235609