A Nonconforming Immersed Finite Element Method for Elliptic Interface Problems

A new immersed finite element (IFE) method is developed for second-order elliptic problems with discontinuous diffusion coefficient. The IFE space is constructed based on the rotated- Q 1 nonconforming finite elements with the integral-value degrees of freedom. The standard nonconforming Galerkin me...

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Bibliographic Details
Published in:Journal of scientific computing 2019-04, Vol.79 (1), p.442-463
Main Authors: Lin, Tao, Sheen, Dongwoo, Zhang, Xu
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Diffusion coefficient
Discontinuity
Finite element method
Galerkin method
Interfaces
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Norms
Theoretical
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Summary:A new immersed finite element (IFE) method is developed for second-order elliptic problems with discontinuous diffusion coefficient. The IFE space is constructed based on the rotated- Q 1 nonconforming finite elements with the integral-value degrees of freedom. The standard nonconforming Galerkin method is employed in this IFE method without any stabilization term. Error estimates in energy and L 2 -norms are proved to be better than O ( h | log h | ) and O ( h 2 | log h | ) , respectively, where the | log h | factors reflect jump discontinuity. Numerical results are reported to confirm our analysis.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-018-0865-9