Suitable weak solutions of the Navier-Stokes equations constructed by a space-time numerical discretization
Analysis of PDEs
2019-05-13 v2 Numerical Analysis
Abstract
We prove that weak solutions obtained as limits of certain numerical space-time discretizations are suitable in the sense of Scheffer and Caffarelli-Kohn-Nirenberg. More precisely, in the space-periodic setting, we consider a full discretization in which the theta-method is used to discretize the time variable, while in the space variables we consider appropriate families of finite elements. The main result is the validity of the so-called local energy inequality.
Keywords
Cite
@article{arxiv.1710.01579,
title = {Suitable weak solutions of the Navier-Stokes equations constructed by a space-time numerical discretization},
author = {Luigi C. Berselli and Simone Fagioli and Stefano Spirito},
journal= {arXiv preprint arXiv:1710.01579},
year = {2019}
}
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16 pages