Skip to content
Licensed Unlicensed Requires Authentication Published online by De Gruyter October 4, 2023

Three Low Order H-Curl-Curl Finite Elements on Triangular Meshes

  • Shangyou Zhang ORCID logo EMAIL logo

Abstract

We construct three H-curl-curl finite elements. The P 2 and P 3 vector finite element spaces are both enriched by one common P 4 bubble and their local degrees of freedom are 13 and 21, respectively. As there does not exist any P 1 H-curl-curl conforming finite element, the P 1 H-curl-curl nonconforming finite element is constructed with three additional P 4 bubbles. Numerical tests are presented, confirming the conformity and the optimal order of convergence.

MSC 2020: 65N15; 65N30

References

[1] V. Girault and P.-A. Raviart, Finite Element Methods for Navier–Stokes Equations. Theory and Algorithms, Springer Ser. Comput. Math. 5, Springer, Berlin, 1986. 10.1007/978-3-642-61623-5Search in Google Scholar

[2] K. Hu, Q. Zhang and Z. Zhang, Simple curl-curl-conforming finite elements in two dimensions, SIAM J. Sci. Comput. 42 (2020), no. 6, A3859–A3877. 10.1137/20M1333390Search in Google Scholar

[3] L. R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp. 54 (1990), no. 190, 483–493. 10.1090/S0025-5718-1990-1011446-7Search in Google Scholar

[4] L. Wang, Q. Zhang, J. Sun and Z. Zhang, A priori and a posterior error estimations of quad-curl eigenvalue problems in 2D, preprint (2020), https://arxiv.org/abs/2007.01330. Search in Google Scholar

[5] Q. Zhang, L. Wang and Z. Zhang, H(curl2)-conforming finite elements in 2 dimensions and applications to the quad-curl problem, SIAM J. Sci. Comput. 41 (2019), no. 3, A1527–A1547. 10.1137/18M1199988Search in Google Scholar

[6] B. Zheng, Q. Hu and J. Xu, A nonconforming finite element method for fourth order curl equations in R3, Math. Comp. 80 (2011), no. 276, 1871–1886. 10.1090/S0025-5718-2011-02480-4Search in Google Scholar

Received: 2022-12-01
Accepted: 2023-08-03
Published Online: 2023-10-04

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 3.5.2024 from https://www.degruyter.com/document/doi/10.1515/cmam-2023-0140/html
Scroll to top button