Two-order superconvergence for a weak Galerkin method on rectangular and cuboid grids
Date
2022-09-22
Journal Title
Journal ISSN
Volume Title
Publisher
Numerical Methods for Partial Differential Equations
Abstract
This article introduces a particular weak Galerkin (WG) element on rectangular/cuboid partitions that uses k $$ k $$ th order polynomial for weak finite element functions and ( k + 1 ) $$ \left(k+1\right) $$ th order polynomials for weak derivatives. This WG element is highly accurate with convergence two orders higher than the optimal order in an energy norm and the L 2 $$ {L}^2 $$ norm. The superconvergence is verified analytically and numerically. Furthermore, the usual stabilizer in the standard weak Galerkin formulation is no longer needed for this element.
Description
This is the peer reviewed version of the following article: Wang, J., Wang, X., Ye, X., Zhang, S., Zhu, P., Two-order superconvergence for a weak Galerkin method on rectangular and cuboid grids, Numer. Methods Partial Differ. Eq.. (2022), 1– 15. https://doi.org/10.1002/num.22918, which has been published in final form at https://doi.org/10.1002/num.22918. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited. This article will be embargoed until 09/22/2023.
Keywords
finite element, weak Galerkin method, second-order elliptic problems, stabilizer-free, rectangular mesh
Citation
Wang, J., Wang, X., Ye, X., Zhang, S., Zhu, P., Two-order superconvergence for a weak Galerkin method on rectangular and cuboid grids, Numer. Methods Partial Differ. Eq.. (2022), 1– 15. https://doi.org/10.1002/num.22918