The conference paper Error Boundedness of Correction Procedure via Reconstruction/Flux Reconstruction and the Connection to Residual Distribution Schemes of Rémi Abgrall, Elise le Mélédo, Philipp Öffner, and me has been published.
We focus on the correction procedure via reconstruction (CPR) / flux reconstruction (FR) methods for hyperbolic conservation laws. Their long time error behavior is investigated and their connection with the Residual Distribution schemes is pointed out. Considering a model problem, we start by deriving an error equation that will be investigated in detail. There, we show that the choice between upwinding and central numerical fluxes affects the growth rate and asymptotic value of the error. Furthermore, the selection of the bases themselves (Gauß-Lobatto-Legendre or auß-Legendre) highly impacts the solution. In particular, using Gauß-Legendre basis, the error reaches the asymptotic value faster than using Gauß-Lobatto-Legendre basis, which also appears to be smaller. In the second part of this contribution, we demonstrate that FR schemes can be transformed into the Residual Distribution (RD) framework and vice versa. As a consequence, we can directly apply the known results from RD schemes to CPR/FR methods.