Flux Recovery and Superconvergence of Quadratic Immersed Interface Finite Elements
It provides a theoretical and numerical framework for improving flux accuracy in immersed finite element methods, which is important for problems with interfaces in computational mechanics.
This paper introduces a flux recovery scheme for quadratic immersed finite element methods, achieving superconvergence at end nodes and interface points, with third-order flux error in the general case and zero error for piecewise constant diffusion without absorption.
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.