A superconvergent CDG finite element for the Poisson equation on polytopal meshes
Date
2023-12-08
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Zeitschrift für anorganische und allgemeine Chemie | Journal of Inorganic and General Chemistry
Abstract
A conforming discontinuous Galerkin (CDG) finite element is constructed for solving second order elliptic equations on polygonal and polyhedral meshes. The numerical trace on the edge between two elements is no longer the average of two discontinuous Pk functions on the two sides, but a lifted Pk+2 function from four Pk functions. When the numerical gradient space is the H (div,T) subspace of piecewise Pdk+1 polynomials on subtriangles/subtehrahedra of a polygon/polyhedron T which have a one-piece polynomial divergence on T, this CDG method has a superconvergence of order two above the optimal order. Due to the superconvergence, we define a post-process which lifts a Pk CDG solution to a quasi-optimal Pk+2 solution on each element. Numerical examples in 2D and 3D are computed and the results confirm the theory.
Description
This is the peer reviewed version of the following article: Ye, X., Zhang, S.: A superconvergent CDG finite element for the Poisson equation on polytopal meshes. Z Angew Math Mech. 00, e202300521 (2023). https://doi.org/10.1002/zamm.202300521, which has been published in final form at https://doi.org/10.1002/zamm.202300521. 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. © 2023 Wiley-VCH GmbH. This article will be embargoed until 12/08/2024.
Keywords
Citation
Ye, X., Zhang, S.: A superconvergent CDG finite element for the Poisson equation on polytopal meshes. Z Angew Math Mech. 00, e202300521 (2023). https://doi.org/10.1002/zamm.202300521