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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
BibTeX@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} }
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