TY - JOUR

T1 - A POSTERIORI ERROR ESTIMATES for SELF-SIMILAR SOLUTIONS to the EULER EQUATIONS

AU - Bressan, Alberto

AU - Shen, Wen

N1 - Funding Information:
The authors would like to thank Ludmil Zikatanov (Mathematics Department, Penn State University) for useful discussions.

PY - 2021/1

Y1 - 2021/1

N2 - 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.

AB - 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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U2 - 10.3934/dcds.2020168

DO - 10.3934/dcds.2020168

M3 - Article

AN - SCOPUS:85083010994

VL - 41

SP - 113

EP - 130

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 1

ER -