Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations

摘要: The purpose of this paper is to provide new insights on the connections that exist between discontinuous Galerkin method (DG), flux reconstruction (FR) and recently identified energy stable (ESFR) when solving time dependent conservation laws. All these schemes appear be quite similar it important understand how they are related. In paper, we first review results stability extend filtered method. We then consider approach show its with DG. particular, Energy Stable Flux Reconstruction introduced by Vincent et al. equivalent a DG method, hence giving proof stability. Also, allows use without having know special form correction polynomials. Finally, underline some fundamental differences FR