Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Robust finite difference schemes for a nonlinear variational wave equation modeling liquid crystals

by F. Weber

(Report number 2013-43)

Abstract
We consider a nonlinear variational wave equation that models the dynamics of nematic liquid crystals. Finite difference schemes that either conserve or dissipate a discrete version of the energy associated with these equations are designed. Numerical experiments in one and two-space dimensions illustrating the stability and efficiency of the schemes are presented. An interesting feature of these schemes is their ability to approximate both the conservative as well as the dissipative weak solutions of the underlying system.

Keywords: Variational wave equation, Conservative, Dissipative, Finite differences

@Techreport{W13_541,
  author = {F. Weber},
  title = {Robust finite difference schemes for a nonlinear variational wave equation modeling liquid crystals},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2013-43},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2013/2013-43.pdf },
  year = {2013}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).