A Posteriori Error Estimates for Self-Similar Solutions to the Euler Equations
Analysis of PDEs
2020-02-07 v1
Abstract
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.
Cite
@article{arxiv.2002.01962,
title = {A Posteriori Error Estimates for Self-Similar Solutions to the Euler Equations},
author = {Alberto Bressan and Wen Shen},
journal= {arXiv preprint arXiv:2002.01962},
year = {2020}
}