Flux Recovery and Superconvergence of Quadratic Immersed Interface Finite Elements

We introduce a flux recovery scheme for the computed solution of a quadratic immersed finite element method. The recovery is done at nodes and interface point first and by interpolation at the remaining points. We show that the end nodes are superconvergence points for both the primary variable $p$ and its flux $u$. Furthermore, in the case of piecewise constant diffusion coefficient without the absorption term the errors at end nodes and interface point in the approximation of $u$ and $p$ are zero. In the general case, flux error at end nodes and interface point is third order. Numerical results are provided to confirm the theory.