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A P 2 H-Div-Nonconforming-H-Curl Finite Element for the Stokes Equations on Triangular Meshes

  • Yunqing Huang , Xuejun Xu and Shangyou Zhang ORCID logo EMAIL logo
Published/Copyright: October 2, 2024

Abstract

The P2 BDM H-div finite element is enriched by five P 5 divergence-free bubbles on each triangle. The resulting finite element remains H-div and is also H-curl nonconforming. Thus the new finite element combined with the discontinuous P 1 element for pressure, is stabilizer-free and still divergence-free in solving the Stokes equations on triangular meshes. The stabilization can also be done by three, four, or six P 5 divergence-free bubble-enrichment each triangle, shown both in theory and in computation. Numerical tests show the advantage of the divergence-free element over the P 2 Taylor–Hood finite element.

MSC 2020: 65N15; 65N30; 76M10

Award Identifier / Grant number: 2020 YFA 0713500

Award Identifier / Grant number: 11971410

Award Identifier / Grant number: 12071350

Award Identifier / Grant number: 12331015

Funding statement: Yunqing Huang was supported in part by National Natural Science Foundation of China (11971410) and China’s National Key R&D Programs (2020 YFA 0713500). Xuejun Xu was supported by National Natural Science Foundation of China (12071350, 12331015).

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Received: 2024-04-18
Revised: 2024-07-09
Accepted: 2024-09-10
Published Online: 2024-10-02
Published in Print: 2025-04-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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