TY - JOUR
T1 - A POSTERIORI ERROR ESTIMATES for SELF-SIMILAR SOLUTIONS to the EULER EQUATIONS
AU - Bressan, Alberto
AU - Shen, Wen
N1 - Publisher Copyright:
© 2021 American Institute of Mathematical Sciences. All rights reserved.
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
SN - 1078-0947
VL - 41
SP - 113
EP - 130
JO - Discrete and Continuous Dynamical Systems- Series A
JF - Discrete and Continuous Dynamical Systems- Series A
IS - 1
ER -