Partially Discontinuous Nodal Finite Elements for 𝐻(curl) and 𝐻(div)-Reference-Cited by-同舟云学术

Partially Discontinuous Nodal Finite Elements for 𝐻(curl) and 𝐻(div)

Published:2022-06-09 Issue:3 Volume:22 Page:613-629
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Hu Jun¹,Hu Kaibo²,Zhang Qian³^ORCID

Affiliation:

1. LMAM and School of Mathematical Sciences , Peking University , Beijing 100871 , P. R. China

2. Mathematical Institute , University of Oxford , Andrew Wiles Building, Radcliffe Observatory Quarter , Oxford , OX2 6GG , United Kingdom

3. Department of Mathematical Sciences , Michigan Technological University , Houghton , MI 49931 , USA

Abstract

Abstract We investigate the discretization of H ⁢ ( curl )

H(\mathrm{curl})

and H ⁢ ( div )

H(\mathrm{div})

in two and three space dimensions by partially discontinuous nodal finite elements, i.e., vector-valued Lagrange finite elements with discontinuity in certain directions. These spaces can be implemented as a combination of continuous and discontinuous Lagrange elements and fit in de Rham complexes. We construct well-conditioned nodal bases.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2022-0053/pdf

Reference49 articles.

1. M. Ainsworth and J. Coyle, Hierarchic h ⁢ p hp -edge element families for Maxwell’s equations on hybrid quadrilateral/triangular meshes, Comput. Methods Appl. Mech. Engrg. 190 (2001), no. 49–50, 6709–6733.

2. M. Ainsworth and S. Jiang, Preconditioning the mass matrix for high order finite element approximation on tetrahedra, SIAM J. Sci. Comput. 43 (2021), no. 1, A384–A414.

3. D. N. Arnold, Finite Element Exterior Calculus, CBMS-NSF Regional Conf. Ser. in Appl. Math. 93, Society for Industrial and Applied Mathematics, Philadelphia, 2018.

4. D. N. Arnold, R. S. Falk and R. Winther, Differential complexes and stability of finite element methods. II. The elasticity complex, Compatible Spatial Discretizations, IMA Vol. Math. Appl. 142, Springer, New York (2006), 47–67.

5. D. N. Arnold, R. S. Falk and R. Winther, Finite element exterior calculus, homological techniques, and applications, Acta Numer. 15 (2006), 1–155.

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