Relative entropy analysis of the Jin-Xin model: Theory and Numerics

This work studies the linear Jin-Xin relaxation model by means of the relative entropy method, both at the continuous and fully discrete levels. Under the strict subcharacteristic condition, we obtain an O($ϵ$) estimate for the convergence toward the equilibrium transport equation. We then develop discrete relative entropy estimates for a Lie splitting scheme and an asymptotic preserving staggered scheme. A fixed-time analysis further explains the O($ϵ$^2 ) behavior observed in the strongly stiff regime and the transition occurring when $ϵ$ becomes comparable to the time step.