A flux preserving immersed nonconforming finite element method for elliptic problems

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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 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. © 2014 Published by Elsevier B.V. onbehalf of IMACS.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2014-07
Language
English
Article Type
Article
Keywords

INTERFACE PROBLEMS; APPROXIMATION CAPABILITY; DISCONTINUOUS GALERKIN; SPACE

Citation

APPLIED NUMERICAL MATHEMATICS, v.81, pp.94 - 104

ISSN
0168-9274
DOI
10.1016/j.apnum.2013.11.007
URI
http://hdl.handle.net/10203/189977
Appears in Collection
MA-Journal Papers(저널논문)
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