The entropy-based moment method is a well-known discretization for the velocity variable in kinetic equations which has many desirable theoretical properties but is difficult to implement with high-order numerical methods. The regularized entropy-based moment method was recently introduced to remove one of the main challenges in the implementation of the entropy-based moment method, namely the requirement of the realizability of the numerical solution. In this work we use the method of relative entropy to prove the convergence of the regularized method to the original method as the regularization parameter goes to zero and give convergence rates. Our main assumptions are the boundedness of the velocity domain and that the original moment solution is Lipschitz continuous in space and bounded away from the boundary of realizability. We provide results from numerical simulations showing that the convergence rates we prove are optimal.

翻译：以 entropy 为基础的瞬时法是动动方程中速度变量的一个众所周知的离散法,它有许多可取的理论属性,但很难用高阶数字方法加以执行。最近采用了基于正态的 entropy 瞬时法,以消除执行基于 entropy 瞬时法的主要挑战之一,即数字解决方案的可变性要求。在这项工作中,我们使用相对的 entropy 方法来证明正规化方法与原方法的趋同,因为正规化参数是零,并具有趋同率。我们的主要假设是速度域的界限,最初的瞬时法是Lipschitz在空间持续,并与真实性边界隔开。我们提供了数字模拟的结果,表明我们所证明的趋同率是最佳的。