论文标题
通过耗散弱解的不连续的Galerkin方案为Euler方程的收敛性
Convergence of Discontinuous Galerkin Schemes for the Euler Equations via Dissipative Weak Solutions
论文作者
论文摘要
在本文中，我们介绍了基于高阶元素方法的收敛分析，特别是我们使用逐个零件运算符的不连续的Galerkin方案进行了关注。为此，至关重要的是，结构保存特性，例如阳性保存和熵不等式。我们演示了如何确保它们并通过耗散弱解决方案证明我们多维高级DG方案的收敛性。在数值模拟中，我们验证了理论结果。
In this paper, we present convergence analysis of high-order finite element based methods, in particular, we focus on a discontinuous Galerkin scheme using summation-by-parts operators. To this end, it is crucial that structure preserving properties, such as positivity preservation and entropy inequality hold. We demonstrate how to ensure them and prove the convergence of our multidimensional high-order DG scheme via dissipative weak solutions. In numerical simulations, we verify our theoretical results.
