IJPAM: Volume 109, No. 3 (2016)

NEW $H^{1}(\Omega)$ CONFORMING FINITE ELEMENTS
ON HEXAHEDRA

Ji Hyun Kim
Department of Mathematics
Hannam University
133 Ojeong-dong, Daedeok-gu, Daejeon 306-791, REPUBLIC OF KOREA

Abstract. In this paper, we introduce new scalar finite element spaces on hexahedron. We prove the unisolvence of degrees of freedom and analyze our spaces using the discrete de Rham diagram.

Received: June 23, 2016

Revised: September 20, 2016

Published: October 1, 2016

AMS Subject Classification: 65N30, 65N25

Key Words and Phrases: finite element methods, $H^{1}$ conforming elements, curl conforming elements, de Rham diagram
Download paper from here.

Bibliography

1
Peter Monk, Finite Element Methods for Maxwell's Equations, Clarendon press, Oxford (2003).

2
Peter Monk and L. Demkowicz, Discrete compactness and the approximation of Maxwell's equations in $R^{3}$, Math. Comp., 70 (2001), 507-523.

3
A. Bossavit, Mixed finite elements and the complex of Whitney forms, Academic press, London (1988).

4
A. Bossavit, Computational Electromagnetism, Academic press, San Diego (1998).

5
Philippe G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland Publishing Company, New York (1978).

6
J. H. Kim and Do Y. Kwak, New curl conforming finite elements on parallelepiped, Numer. Math., 131 (2015), 473-488, doi: 10.1007/s00211-015-0696-7.

7
J. Douglas Jr. and J. E. Roberts, Mixed finite element methods for second order elliptic problems, Math. Apl. Comput., 1 (1989), 91-103.

8
J. H. Kim, New $H^{1}(\Omega)$ conforming finite element spaces, IJPAM , 91 (2014), 245-252, doi: https://dx.doi.org/10.12732/ijpam.v91i2.11.

.




DOI: 10.12732/ijpam.v109i3.10 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 3
Pages: 609 - 617


$H^{1}(\Omega)$ CONFORMING FINITE ELEMENTS ON HEXAHEDRA%22&as_occt=any&as_epq=&as_oq=&as_eq=&as_publication=&as_ylo=&as_yhi=&as_sdtAAP=1&as_sdtp=1" title="Click to search Google Scholar for this entry" rel="nofollow">Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).