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 ...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 bihnear 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.展开更多
基金supported by NSF grant DMS-0713763the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 501709)the AMSS-PolyU Joint Research Institute for Engineering and Management Mathematics, and NSERC (Canada)
文摘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 bihnear 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.
