A Crank-Nicolson type minimization scheme for a hyperbolic free boundary problem
Numerical Analysis
2021-05-12 v2 Numerical Analysis
Abstract
We consider a hyperbolic free boundary problem by means of minimizing time discretized functionals of Crank-Nicolson type. The feature of this functional is that it enjoys energy conservation in the absence of free boundaries, which is an essential property for numerical calculations. The existence and regularity of minimizers is shown and an energy estimate is derived. These results are then used to show the existence of a weak solution to the free boundary problem in the 1-dimensional setting.
Cite
@article{arxiv.2004.07458,
title = {A Crank-Nicolson type minimization scheme for a hyperbolic free boundary problem},
author = {Yoshiho Akagawa and Elliott Ginder and Syota Koide and Seiro Omata and Karel Svadlenka},
journal= {arXiv preprint arXiv:2004.07458},
year = {2021}
}
Comments
21 pages, 6 figures