A Divergence-Free Pk CDG Finite Element for the Stokes Equations on Triangular and Tetrahedral Meshes
Date
2024-11
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Numerical Mathematics: Theory, Methods and Applications
Abstract
In the conforming discontinuous Galerkin method, the standard bilinear form for the conforming finite elements is applied to discontinuous finite elements without adding any inter-element nor penalty form. The Pk (k ≥ 1) discontinuous finite elements and the Pk−1 weak Galerkin finite elements are adopted to approximate the velocity and the pressure respectively, when solving the Stokes equations on triangular or tetrahedral meshes. The discontinuous finite element solutions are divergence-free and surprisingly H-div functions on the whole domain. The optimal order convergence is achieved for both variables and for all k ≥ 1. The theory is verified by numerical examples.
Description
First published in Numerical Mathematics: Theory, Methods and Applications in November 2024, published by Global Science Press. The version of record is available at: https://doi.org/10.4208/nmtma.OA-2024-0063.
©2024 Global-Science Press.
Keywords
finite element, conforming discontinuous Galerkin method, Stokes equations, sta- bilizer free, divergence free
Citation
Zhang, Xiu Ye And Shangyou. “A Divergence-Free Pk CDG Finite Element for the Stokes Equations on Triangular and Tetrahedral Meshes.” Numerical Mathematics: Theory, Methods and Applications 0, no. 0 (November 2024): 0–0. https://doi.org/10.4208/nmtma.OA-2024-0063.