An analysis of stability of the flux reconstruction formulation on quadrilateral elements for the linear advection-diffusion equation (Q1743439)

The stability of the flux reconstruction approach to high-order methods applied for linear advection-diffusion equation is analysed. The authors present an extension of the 1D stability analysis for the case of tensor product elements like quadrilaterals overcoming several difficulties as using a different norm from that on of 1D problem. It is shown that these flux reconstruction schemes are stable for the linear advection-diffusion equation on Cartesian meshes. The analysis in this paper also provides additional insights into the choice of a numerical method parameter and stability characteristics of these schemes. Numerical results are shown supporting the theoretical findings.