A Posteriori Error Estimates for Self-Similar Solutions to the Euler Equations

Alberto Bressan; Wen Shen

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arXiv · 2002.01962

A Posteriori Error Estimates for Self-Similar Solutions to the Euler Equations

Alberto Bressan·Wen Shen

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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.

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Alberto Bressan, Wen Shen. 2020-02-05. A Posteriori Error Estimates for Self-Similar Solutions to the Euler Equations. https://arxiv.org/abs/2002.01962

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