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

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

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)2661-2681
Number of pages21
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume27
Issue number5
DOIs
Publication statusPublished - May 2022

Keywords

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

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