金鑫模型的相对熵分析：理论与数值方法
Relative entropy analysis of the Jin-Xin model: Theory and Numerics
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中文总结 AI 辅助
研究线性金鑫松弛模型，用相对熵方法在连续和全离散层面分析，获收敛估计，建立格式的离散相对熵估计，通过固定时间分析解释强刚性区域行为及$\epsilon$与时间步长可比时的转变。
中文摘要 AI 辅助
本文通过相对熵方法在连续和全离散层面研究线性金鑫松弛模型。在严格次特征条件下，得到向平衡输运方程收敛的O($\epsilon$)估计。接着为李分裂格式和渐近保持交错格式建立离散相对熵估计。固定时间分析进一步解释了在强刚性区域观察到的O($\epsilon$^2 )行为以及当$\epsilon$与时间步长可比时的转变。
英文摘要
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.
