Higher-order immersed discontinuous Galerkin methods

We propose new discontinuous finite element methods that can be applied to one-dimensional elliptic problems with discontinuous coeffi-cients. These methods are based on a class of higher degree immersed finite element spaces and can be used with a mesh independent of the location of coefficient discontinuity. Numerical experiments are pre-sented to show that these methods can achieve optimal convergence rates under both h and p refinements.