Multiscale Modeling &Simulation, Volume 19, Issue 2, Page 802-829, January 2021.
The Lagrange-multiplier technique is a multiscale numerical scheme designed to solve evolution problems containing some stiff transport terms. Such multiscale problems arise very often in kinetic models for the description of thermonuclear plasma dynamics. The particularity of this scheme is that it permits one to capture (without having to refine the discretization) even the asymptotic limit when the small parameter $\varepsilon$ describing the stiffness of the problem goes to zero. This property is called asymptotic-preserving and has been validated numerically in previous works of the author. In the present work, the missing mathematical study of this Lagrange-multiplier approach is performed, with special emphasis on the asymptotic limit when $\varepsilon \rightarrow 0$.

中文翻译：

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刚性输运问题的拉格朗日乘子技术的数学研究

多尺度建模与仿真，第 19 卷，第 2 期，第 802-829 页，2021 年 1 月。
拉格朗日乘子技术是一种多尺度数值方案，旨在解决包含一些刚性输运项的演化问题。这种多尺度问题经常出现在描述热核等离子体动力学的动力学模型中。该方案的特殊性在于，当描述问题刚度的小参数 $\varepsilon$ 变为零时，它甚至可以捕获（无需细化离散化）渐近极限。这个特性被称为渐近保持性，并且已经在作者以前的作品中进行了数值验证。在目前的工作中，对这种拉格朗日乘子方法进行了缺失的数学研究，特别强调了 $\varepsilon \rightarrow 0$ 时的渐近极限。