Interior Penalty Bilinear Ife Discontinuous Galerkin Methods for Elliptic Equations with Discontinuous Coefficient
This paper applies bilinear immersed finite elements (IFEs) in the interior penalty discontinuous Galerkin (DG) methods for solving a second order elliptic equation with discontinuous coefficient. A discontinuous bilinear IFE space is constructed and applied to both the symmetric and nonsymmetric interior penalty DG formulations. The new methods can solve an interface problem on a Cartesian mesh independent of the interface with local refinement at any locations needed even if the interface has a nontrivial geometry. Numerical examples are provided to show features of these methods.
X. He et al., "Interior Penalty Bilinear Ife Discontinuous Galerkin Methods for Elliptic Equations with Discontinuous Coefficient," Journal of Systems Science and Complexity, Springer Verlag, Jan 2010.
The definitive version is available at https://doi.org/10.1007/s11424-010-0141-z
Mathematics and Statistics
Keywords and Phrases
adaptive mesh; discontinuous Galerkin; immersed interface; interface problems; penalty
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