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 discontinuousGalerkin (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 nonsymmetricinterior penalty DG formulations.The new methods can solve an interface problem on a Cartesianmesh independent of the interface with local refinement at any locations needed even if the interfacehas a nontrivial geometry.Numerical examples are provided to show features of these methods.