Abstract
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.
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