Open AccessA Crank-Nicolson type minimization scheme for a hyperbolic free boundary problem
Author(s) -
Yoshiho Akagawa,
Elliott Ginder,
Syota Koide,
Seiro Omata,
Karel Švadlenka
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021153
Subject(s) - discretization , mathematics , crank–nicolson method , type (biology) , boundary (topology) , free boundary problem , energy (signal processing) , property (philosophy) , boundary value problem , minification , scheme (mathematics) , mathematical analysis , mathematical optimization , ecology , statistics , philosophy , epistemology , biology
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.