[KSCI] Korea Science Citation Index Service

KIM, JI HYUN (Department of Mathematics, Hannam University)

Publication Information

Abstract

In this paper, we prove the discrete compactness property for Kim-Kwak finite element spaces of any order under a weak quasi-uniformity assumption.

Keywords

Discrete compactness property; edge finite elements; Maxwell's eigenvalue problem;

Citations & Related Records

1	J. Nedelec, Mixed finite elements in $R^{3}$ , Numer. Math. 35, 3 (1980), 315-341. https://doi.org/10.1007/BF01396415 DOI
2	R. Leis, Initial Boundary Value Problems in Mathematical Physics, John Wiley, New York, 1986.
3	P. Monk and L. Demkowicz, Discrete compactness and the approximation of Maxwell's equations in $R^{3}$ , Mathematics of Computation 70, 234 (2000), 507-523. https://doi.org/s0025-5718(00)01229-1 DOI
4	M. Costabel and M. Dauge, Singularities of electromagnetic fields in polyhedral domains, tech. report, IRMAR, Universite de Rennes 1, 1997.
5	F. Kikuchi, An isomorphic property of two Hilbert spaces appearing in electromagnetism: Analysis by the mixed formulation, Japan J. Appl. Math. 3 (1986), 53-58. https://doi.org/10.1007/BF03167091 DOI
6	F. Kikuchi, Mixed and penalty formulations for finite element analysis of an eigenvalue problem in electromagnetism, Comput. Methods Appl. Mech. Eng. 64 (1987), 509-521. https://doi.org/10.1016/0045-7825(87)90053-3 DOI
7	F. Kikuchi, On a discrete compactness property for the Nedelec finite elements, J. Fac. Sci. Univ. Tokyo, Sect. 1A, Math. 36 (1989), 479-490.
8	J.H. Kim and Do Y. Kwak, New curl conforming finite elements on parallelepiped, Numer. Math. 131 (2015), 473-488. https://doi.org/10.1007/s00211-015-0696-7 DOI
9	J.H. Kim, New $H^1$ ( $\Omega$ ) conforming finite elements on hexahedra, IJPAM 109, 3 (2016), 609-617. https://doi.org/10.12732/ijpam.v109i3.10