A Selective Immersed Discontinuous Galerkin Method for Elliptic Interface Problems
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.
X. He et al., "A Selective Immersed Discontinuous Galerkin Method for Elliptic Interface Problems," Mathematical Methods in the Applied Sciences, vol. 37, no. 7, pp. 983-1002, John Wiley & Sons Ltd, Jan 2013.
The definitive version is available at https://doi.org/10.1002/mma.2856
Mathematics and Statistics
Center for High Performance Computing Research
Keywords and Phrases
Geometry; Problem Solving; Discontinuous Galerkin; Immersed Finite Elements; Interface Problems; Mesh Refinement; Penalty; Galerkin Methods
International Standard Serial Number (ISSN)
Article - Journal
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