A flux preserving immersed nonconforming finite element method for elliptic problems

An immersed nonconforming finite element method based on the flux continuity on intercell boundaries is introduced. The direct application of flux continuity across the support of basis functions yields a nonsymmetric stiffness system for interface elements. To overcome non-symmetry of the stiffness...

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Bibliographic Details
Published in:Applied numerical mathematics 2014-07, Vol.81, p.94-104
Main Authors: Jeon, Youngmok, Kwak, Do Young
Format: Article
Language:English
Subjects:
Boundaries
Continuity
Convergence
Finite element method
Flux
Hybridization
Immersed finite element
Mathematical analysis
Mathematical models
Stiffness
Symmetrization
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Summary:An immersed nonconforming finite element method based on the flux continuity on intercell boundaries is introduced. The direct application of flux continuity across the support of basis functions yields a nonsymmetric stiffness system for interface elements. To overcome non-symmetry of the stiffness system we introduce a modification based on the Riesz representation and a local postprocessing to recover local fluxes. This approach yields a P1 immersed nonconforming finite element method with a slightly different source term from the standard nonconforming finite element method. The recovered numerical flux conserves total flux in arbitrary sub-domain. An optimal rate of convergence in the energy norm is obtained and numerical examples are provided to confirm our analysis.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2013.11.007