Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 37, Issue 7, Pages 983-1002Publisher
WILEY
DOI: 10.1002/mma.2856
Keywords
interface problems; penalty; selective discontinuous Galerkin; mesh refinement; immersed finite elements
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Funding
- National Science Foundation (NSF) [DMS-0713763]
- National Science Foundation of China [10875034, 11175052]
- General Research Fund (GRF) of Hong Kong Special Administrative Region (HKSAR) [501012]
- Natural Sciences and Engineering of Canada (NSERC)
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This article proposes a selective immersed discontinuous Galerkin method based on bilinear immersed finite elements (IFE) for solving second-order elliptic interface problems. This method applies the discontinuous Galerkin formulation wherever selected, such as those elements around an interface or a singular source, but the regular Galerkin formulation everywhere else. A selective bilinear IFE space is constructed and applied to the selective immersed discontinuous Galerkin method based on either the symmetric or nonsymmetric interior penalty discontinuous Galerkin formulation. The new method can solve an interface problem by a rectangular mesh with local mesh refinement independent of the interface even if its geometry is nontrivial. Meanwhile, if desired, its computational cost can be maintained very close to that of the standard Galerkin IFE method. It is shown that the selective bilinear IFE space has the optimal approximation capability expected from piecewise bilinear polynomials. Numerical examples are provided to demonstrate features of this method, including the effectiveness of local mesh refinement around the interface and the sensitivity to the penalty parameters. Copyright (c) 2013 John Wiley & Sons, Ltd.
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