Immersed finite element method for eigenvalue problem

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• 作者：Seungwoo Lee^a ; ^{woo528@kaist.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Do Y. Kwak^a ; ^{kdy@kaist.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Imbo Sim^b ; ^{imbosim@nims.re.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Eigenvalue ; Finite elements ; Immersed interface
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：410-426
• 全文大小：1651 K

文摘

We consider the approximation of elliptic eigenvalue problem with an interface. The main aim of this paper is to prove the stability and convergence of an immersed finite element method (IFEM) for eigenvalues using Crouzeix–Raviart class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304551&_mathId=si64.gif&_user=111111111&_pii=S0377042716304551&_rdoc=1&_issn=03770427&md5=8d00bd7d1c674a76fd0623cb776f9a8e" title="Click to view the MathML source">P₁class="mathContainer hidden">class="mathCode">$P_1$-nonconforming approximation. We show that spectral analysis for the classical eigenvalue problem can be easily applied to our model problem. We analyze the IFEM for elliptic eigenvalue problems with an interface and derive the optimal convergence of eigenvalues. Numerical experiments demonstrate our theoretical results.