The Flux Reconstruction approach is a recent high-order method which has been introduced for unsteady problems. Initial energy stability has been conducted for the advection problem, leading to the well know Energy Stable Flux Reconstruction (ESFR) scheme. Using the ESFR scheme, the energy stability proof has been extended for the advection–diffusion using the Local Discontinuous Galerkin (LDG) numerical flux. Recently, stability conditions were derived for the compact Interior Penalty (IP) and Bassi–Rebay II (BR2) numerical fluxes. Here we apply ESFR schemes to elliptic problems and derive the associated bilinear form for the Poisson equation. We show that for the compact IP and BR2 numerical fluxes, the bilinear form is independent of the auxiliary correction function. Finally, we provide some insights on the coercivity of the ESFR scheme.

磁通重构方法是最近针对不稳定问题引入的一种高阶方法。对流问题已经进行了初步的能量稳定，从而产生了众所周知的能量稳定通量重建（ESFR）方案。使用ESFR方案，已使用局部不连续Galerkin（LDG）数值通量扩展了对流扩散的能量稳定性证明。最近，获得了稳定的内部罚分（IP）和Bassi-Rebay II（BR2）数值通量的稳定性条件。在这里，我们将ESFR方案应用于椭圆问题，并推导Poisson方程的相关双线性形式。我们表明，对于紧凑的IP和BR2数值通量，双线性形式独立于辅助校正函数。最后，我们对ESFR方案的矫顽力提供了一些见解。