Journal of Hebei University of Water Resources and Electric Engineering

Journal of Hebei University of Water Resources and Electric Engineering ›› 2020, Vol. 30 ›› Issue (1): 67-73.DOI: 10.16046/j.cnki.issn2096-5680.2020.01.013

• Basic Science Research Column • Previous Articles     Next Articles

Discrete Quasi-norm Equivalence Theorem of Two-dimensional H(div)and H(curl)Spaces to Their Trace Spaces

HUO Zhi-xin，WANG Meng，WANG Yuan-yuan，KONG De-zhi   

  1. Foundation Department，Hebei University of Water Resources and Electric Engineering，061001，Cangzhou，Hebei，China
  • Received:2019-08-19 Revised:2019-10-12 Online:2020-03-31 Published:2020-04-30

二维H(div)和H(curl)空间到其迹空间的离散的拟范数等价定理

霍志鑫，王 猛，王园园，孔德志   

  1. 河北水利电力学院基础部，河北省沧州市重庆路1号 061001
  • 作者简介:霍志鑫(1988-)，女，河北邢台市人，助教，现从事高等数学教育工作，研究方向计算数学｡E-mail:zhixinhuo@126.com

PDF

Abstract: In this paper，the discrete harmonic extension theorem of the corresponding trace space H-1/2(∂Ω)into the two-dimensional H(div;Ω)and H(div;Ω)space is proved in detail，and the discrete quasinorm equivalence theorem of the two-dimensional H(div;Ω)and H(curl;Ω)space to the corresponding trace space H-1/2(∂Ω)is obtained，which plays an important role in theoretical analysis and the design of numerical calculation methods.

Key words: two-dimensional H(div, Ω)space, two dimensional H(curl, Ω)space, discrete harmonic extension theorem H-1/2(?Ω), discrete trace theorem, discrete quasi-norm equivalence theorem

摘要： 文中给出了相应迹空间H~(-1/2)(?Ω)到二维H(div;Ω)和H(curl;Ω)空间的离散的调和延拓定理的证明,从而得到了二维H(div;Ω)和H(curl;Ω)空间到相应迹空间H~(-1/2)(?Ω)的离散的拟范数等价定理,这在理论分析和数值计算方法的设计中有很重要的作用。

关键词:  , 二维H(div, Ω)空间, 二维H(curl, Ω)空间, 迹空间H~(-1/2)(?Ω), 离散的调和延拓定理, 离散迹定理, 离散的拟范数等价定理

CLC Number: