论文标题
欧拉方程的自相似解决方案的后验错误估计
A Posteriori Error Estimates for Self-Similar Solutions to the Euler Equations
论文作者
论文摘要
本文的主要目的是分析一个“最简单”的初始数据家族，如数值模拟所示，不可压缩的Euler方程具有多个解决方案。我们在这里迈出了对这些数值结果的严格验证的第一步。也就是说，我们考虑了与自相似解决方案相对应的方程系统，该方程仅限于具有光滑边界的有限域。给定通过有限维盖金方法获得的近似解决方案，我们在数值近似与具有相同边界数据的精确解决方案之间建立了后验误差界限。
The main goal of this paper is to analyze a family of "simplest possible" initial data for which, as shown by numerical simulations, the incompressible Euler equations have multiple solutions. We take here a first step toward a rigorous validation of these numerical results. Namely, we consider the system of equations corresponding to a self-similar solution, restricted to a bounded domain with smooth boundary. Given an approximate solution obtained via a finite dimensional Galerkin method, we establish a posteriori error bounds on the distance between the numerical approximation and the exact solution having the same boundary data.
