IJPAM: Volume 91, No. 2 (2014)

NEW $H^{1}(\Omega)$ CONFORMING FINITE ELEMENT SPACES

JiHyun Kim
Department of Mathematics
Hannam University
133 Ojeong-Dong, Daedeok-Gu, Daejeon 306-791, REPUBLIC OF KOREA


Abstract. Discretization of Maxwell's eigenvalue problem with edge finite elements involves a simultaneous use of two discrete subspaces of $H^{1}(\Omega)$ and $H(\mcurl,\Omega)$. In this paper, we introduce new scalar finite element spaces and edge finite element spaces, respectively. We also prove the unisolvence of degrees of freedom and analyze our spaces using the discrete de Rham diagram.

Received: November 29, 2013

AMS Subject Classification: 65N30, 65N25

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

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DOI: 10.12732/ijpam.v91i2.11 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: 2014
Volume: 91
Issue: 2