Geodesic
On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 3, pp. 389-405

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We discretize the nonlinear Schrödinger equation, with Dirichlet boundary conditions, by a linearly implicit two-step finite element method which conserves the L 2 norm. We prove optimal order a priori error estimates in the L 2 and H 1 norms, under mild mesh conditions for two and three space dimensions.

Classification : 65M12, 65M60
Keywords: nonlinear Schrödinger equation, two-step time discretization, linearly implicit method, finite element method, $L^2$ and $H^1$ error estimates, optimal order of convergence 
@article{M2AN_2001__35_3_389_0,
     author = {Zouraris, Georgios E.},
     title = {On the convergence of a linear two-step finite element method for the nonlinear {Schr\"odinger} equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {389--405},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {3},
     year = {2001},
     mrnumber = {1837077},
     zbl = {0991.65088},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_3_389_0/}
}
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Zouraris, Georgios E. On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 3, pp. 389-405. http://geodesic.mathdoc.fr/item/M2AN_2001__35_3_389_0/