English

Numerical conservative solutions of the Hunter--Saxton equation

Analysis of PDEs 2021-05-13 v2 Numerical Analysis Numerical Analysis

Abstract

In the article a convergent numerical method for conservative solutions of the Hunter--Saxton equation is derived. The method is based on piecewise linear projections, followed by evolution along characteristics where the time step is chosen in order to prevent wave breaking. Convergence is obtained when the time step is proportional to the square root of the spatial step size, which is a milder restriction than the common CFL condition for conservation laws.

Keywords

Cite

@article{arxiv.2005.03882,
  title  = {Numerical conservative solutions of the Hunter--Saxton equation},
  author = {Katrin Grunert and Anders Nordli and Susanne Solem},
  journal= {arXiv preprint arXiv:2005.03882},
  year   = {2021}
}