caa a22 4500 378867148 CHVBK 20180305123400.0 cr unu---uuuuu 161128e20031201xx s 000 0 eng 10.1515/156939503322663458 doi (NATIONALLICENCE)gruyter-10.1515/156939503322663458 A penalty approach to the numerical simulation of a constrained wave motion [Elektronische Daten] [R. Glowinski, A. Lapin, S. Lapin] The main goal of this article is to investigate the numerical solution of a vector-valued nonlinear wave equation, the nonlinearity being of the Ginzburg-Landau type, namely (|u|2-1)u. This equation is obtained when treating by penalty a constrained wave-motion, where the displacement vector is of constant length (1 here, after rescaling). An important step of the approximation process is the construction of a time discretization scheme preserving - in some sense - the energy conservation property of the continuous model. The stability properties of the above scheme are discussed. The authors discuss also the finite element approximation and the quasi-Newton solution of the nonlinear elliptic system obtained at each time step from the time discretization. The results of numerical experiments are presented; they show that for the constraint of the original wave problem to be accurately verified we need to use a small value of the penalty parameter. Copyright 2003, Walter de Gruyter Penalty approach nationallicence numerical simulation nationallicence constrainedwave motion nationallicence Glowinski R. University of Houston, Houston, TX, 77204, USA aut Lapin A. Kazan State University, Kazan 420008, Russia aut Lapin S. University of Houston, Houston, TX, 77204, USA aut Journal of Numerical Mathematics Walter de Gruyter 11/4(2003-12-01), 289-300 1570-2820 11:4<289 2003 11 jnma https://doi.org/10.1515/156939503322663458 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939503322663458 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Glowinski R. University of Houston, Houston, TX, 77204, USA aut NATIONALLICENCE 700 1- Lapin A. Kazan State University, Kazan 420008, Russia aut NATIONALLICENCE 700 1- Lapin S. University of Houston, Houston, TX, 77204, USA aut NATIONALLICENCE 773 0- Journal of Numerical Mathematics Walter de Gruyter 11/4(2003-12-01), 289-300 1570-2820 11:4<289 2003 11 jnma CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter