Abstract
In this paper we present a numerical approach to a nonstandard second-order elliptic eigenvalue problem defined on two overlapping rectangular domains with a nonlocal (integral) boundary condition. Usually, for this class of problems error estimates are suboptimal. By introducing suitable degrees of freedom and a corresponding interpolation operator we derive optimal order finite element approximation. Numerical results illustrate the efficiency of the proposed method.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Andreev, A.B., Racheva, M.R.: Optimal order finite element method for coupled eigenvalue problem on overlappingdomains. In: Dimov, I.T., Lirkov, I., Margenov, S., Zlatev, Z. (eds.) NMA 2002. LNCS, vol. 2542, pp. 637–644. Springer, Heidelberg (2003)
De Shepper, H.: Finite element analysis of a coupling eigenvalue problem on overlapping domains. J. Comput. Appl. Math. 132, 141–153 (2001)
Huang, Y.Q., Xu, J.C.: A conforming finite element method for overlapping and nonmatching grids. Math. Comp. 72(243), 1057–1066 (2003)
Cai, X.C., Dryja, M., Sarkis, M.: Overlapping nonmatchinggrids mortar element methods for elliptic problems. SIAM J. Numer. Anal. 36(2), 581–606 (1999)
Raviart, P.A., Thomas, J.M.: Introduction a l’Analyse Numerique des Equations aux Derivees Partielles. Masson Paris (1983)
Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978)
Zienkiewich, O.C., Zhu, J.Z.: The superconvergence patch-recovery (SPR) and adaptive finite element refinement. Comp. Methods Appl. Mech. Eng. 101, 207–224 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Andreev, A.B., Racheva, M.R. (2009). Optimal Order FEM for a Coupled Eigenvalue Problem on 2D Overlapping Domains. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-00464-3_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00463-6
Online ISBN: 978-3-642-00464-3
eBook Packages: Computer ScienceComputer Science (R0)