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

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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.

Original languageEnglish (US)
Pages (from-to)113-130
Number of pages18
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume41
Issue number1
DOIs
StatePublished - Jan 2021

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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