A CRANK-NICOLSON TYPE MINIMIZATION SCHEME FOR A HYPERBOLIC FREE BOUNDARY PROBLEM

Yoshiho Akagawa; Elliott Ginder; Syota Koide; Seiro Omata; Karel Svadlenka

doi:10.3934/dcdsb.2021153

A CRANK-NICOLSON TYPE MINIMIZATION SCHEME FOR A HYPERBOLIC FREE BOUNDARY PROBLEM

Yoshiho Akagawa, Elliott Ginder, Syota Koide, Seiro Omata, Karel Svadlenka

Department of Mathematical Sciences Based on Modeling and Analysis

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a hyperbolic free boundary problem by means of min- imizing time discretized functionals of Crank-Nicolson type. The feature of this functional is that it enjoys energy conservation in the absence of free bound- aries, 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 bound- ary problem in the 1-dimensional setting.

Original language	English
Pages (from-to)	2661-2681
Number of pages	21
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	27
Issue number	5
DOIs	https://doi.org/10.3934/dcdsb.2021153
Publication status	Published - May 2022

Keywords

Crank-Nicolson type functional
discrete Morse flow
energy conservation
Hyperbolic free boundary problem
variational method

Access to Document

10.3934/dcdsb.2021153

Cite this

@article{e8f99fed472246cabe711a6c90d2e8f4,

title = "A CRANK-NICOLSON TYPE MINIMIZATION SCHEME FOR A HYPERBOLIC FREE BOUNDARY PROBLEM",

abstract = "We consider a hyperbolic free boundary problem by means of min- imizing time discretized functionals of Crank-Nicolson type. The feature of this functional is that it enjoys energy conservation in the absence of free bound- aries, 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 bound- ary problem in the 1-dimensional setting.",

keywords = "Crank-Nicolson type functional, discrete Morse flow, energy conservation, Hyperbolic free boundary problem, variational method",

author = "Yoshiho Akagawa and Elliott Ginder and Syota Koide and Seiro Omata and Karel Svadlenka",

note = "Funding Information: Acknowledgments. E. Ginder would like to acknowledge the support of JSPS Kakenhi Grant number 17K14229. The research of the fourth author was partially funded by a joint research project with YKK Corporation. The research of the last author was supported by JSPS Kakenhi Grant numbers 19K03634 and 18H05481. We would also like to thank the anonymous referees for their constructive comments. Publisher Copyright: {\textcopyright} 2022 American Institute of Mathematical Sciences. All rights reserved.",

year = "2022",

month = may,

doi = "10.3934/dcdsb.2021153",

language = "English",

volume = "27",

pages = "2661--2681",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "Southwest Missouri State University",

number = "5",

}

TY - JOUR

T1 - A CRANK-NICOLSON TYPE MINIMIZATION SCHEME FOR A HYPERBOLIC FREE BOUNDARY PROBLEM

AU - Akagawa, Yoshiho

AU - Ginder, Elliott

AU - Koide, Syota

AU - Omata, Seiro

AU - Svadlenka, Karel

N1 - Funding Information: Acknowledgments. E. Ginder would like to acknowledge the support of JSPS Kakenhi Grant number 17K14229. The research of the fourth author was partially funded by a joint research project with YKK Corporation. The research of the last author was supported by JSPS Kakenhi Grant numbers 19K03634 and 18H05481. We would also like to thank the anonymous referees for their constructive comments. Publisher Copyright: © 2022 American Institute of Mathematical Sciences. All rights reserved.

PY - 2022/5

Y1 - 2022/5

N2 - We consider a hyperbolic free boundary problem by means of min- imizing time discretized functionals of Crank-Nicolson type. The feature of this functional is that it enjoys energy conservation in the absence of free bound- aries, 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 bound- ary problem in the 1-dimensional setting.

AB - We consider a hyperbolic free boundary problem by means of min- imizing time discretized functionals of Crank-Nicolson type. The feature of this functional is that it enjoys energy conservation in the absence of free bound- aries, 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 bound- ary problem in the 1-dimensional setting.

KW - Crank-Nicolson type functional

KW - discrete Morse flow

KW - energy conservation

KW - Hyperbolic free boundary problem

KW - variational method

UR - http://www.scopus.com/inward/record.url?scp=85128436831&partnerID=8YFLogxK

U2 - 10.3934/dcdsb.2021153

DO - 10.3934/dcdsb.2021153

M3 - Article

AN - SCOPUS:85128436831

VL - 27

SP - 2661

EP - 2681

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 5

ER -

A CRANK-NICOLSON TYPE MINIMIZATION SCHEME FOR A HYPERBOLIC FREE BOUNDARY PROBLEM

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this