%0 Journal Article
%T 可压欧拉方程高精度数值格式耗散测度值解的收敛性<br>Convergence of Dissipative Measure-Valued Solutions for High Order Numerical Schemes of the Compressible Euler Equations
%A 皇晓燕
%A 华嘉乐
%J Pure Mathematics
%P 458-471
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.154146
%X 本文主要考虑可压欧拉方程组的初边值问题。研究了两类具有高阶精度的熵稳定有限体积格式的收敛性，通过对数值解建立合适的一致性估计，证明随着步长 h → 0，若数值解的密度是远离真空且有界的，则由这两类熵稳定数值格式构造的解可以生成耗散测度值解。<br>In this paper, we primarily consider the initial boundary value problem for compress ible Euler equations. We study the convergence of two classes of high-order accurate entropy stable finite volume schemes. By establishing appropriate the priori esti mates for the numerical solutions, we prove that as the step size h → 0, the solutions
constructed by these two types of entropy stable numerical schemes can generate dissipative measure-valued solutions, provided that the density of the approximate solutions is bounded away from vacuum and bounded above.
%K 可压欧拉系统，耗散测度值解，熵稳定数值格式，Weak BV条件<br>Compressible Euler Equations
%K Dissipative Measure-Valued Solution
%K Entropy Stable Numerical Schemes
%K Weak Bounded Variation Condition
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=113277