On the Convergence of the Spectral Viscosity Method for the Two-Dimensional Incompressible Euler Equations with Rough Initial Data
On the Convergence of the Spectral Viscosity Method for the Two-Dimensional Incompressible Euler Equations with Rough Initial Data
复制标题
粗糙初始数据二维不可压缩欧拉方程谱粘度法的收敛性
DOI：
10.1007/s10208-019-09440-0
复制
发表时间：
2019
影响因子：
3
通讯作者：
Siddhartha Mishra
中科院分区：
文献类型：
--
作者：
S. Lanthaler;Siddhartha Mishra
本文提出了一种谱粘性方法来近似具有粗糙初值的二维Euler方程，并证明了该方法对于一大类初值收敛到弱解，包括当初始涡量在所谓的Delort类中时，即，它是一个有符号测度和一个可积函数的和。这提供了第一个收敛性证明的数值方法近似的欧拉方程与这样的粗糙的初始数据，并关闭可用的存在性理论和严格的收敛性结果的数值方法之间的差距差距。我们还提出了数值实验，包括涡面和约束涡的计算，以说明所提出的方法。
We propose a spectral viscosity method to approximate the two-dimensional Euler equations with rough initial data and prove that the method converges to a weak solution for a large class of initial data, including when the initial vorticity is in the so-called Delort class, i.e., it is a sum of a signed measure and an integrable function. This provides the first convergence proof for a numerical method approximating the Euler equations with such rough initial data and closes the gap between the available existence theory and rigorous convergence results for numerical methods. We also present numerical experiments, including computations of vortex sheets and confined eddies, to illustrate the proposed method.
影响因子：
2.5
作者：
De Lellis, Camillo;Szekelyhidi, Laszlo, Jr.
通讯作者：
Szekelyhidi, Laszlo, Jr.