A Divergence-Free Pk CDG Finite Element for the Stokes Equations on Triangular and Tetrahedral Meshes

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Author(s)Ye, Xiu
Author(s)Zhang, Shangyou
Date Accessioned2025-03-12T16:34:46Z
Date Available2025-03-12T16:34:46Z
Publication Date2024-11
DescriptionFirst 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.
AbstractIn 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.
CitationZhang, 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.
ISSN2079-7338
URLhttps://udspace.udel.edu/handle/19716/35901
Languageen_US
PublisherNumerical Mathematics: Theory, Methods and Applications
Keywordsfinite element
Keywordsconforming discontinuous Galerkin method
KeywordsStokes equations
Keywordssta- bilizer free
Keywordsdivergence free
TitleA Divergence-Free Pk CDG Finite Element for the Stokes Equations on Triangular and Tetrahedral Meshes
TypeArticle
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