On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation
Department of Numerical Analysis
and Computing Science (NADA), Royal Institute of Technology (KTH),
10044 Stockholm, Sweden. : Centre de Recherche en Mathématiques
de la Décision (CEREMADE), UMR CNRS 7534, Université de Paris IX-Dauphine,
Place du Maréchal de Lattre-de-Tassigny, 75775 Paris Cedex 16, France.
We discretize the nonlinear Schrödinger equation, with Dirichlet boundary conditions, by a linearly implicit two-step finite element method which conserves the L2 norm. We prove optimal order a priori error estimates in the L2 and H1 norms, under mild mesh conditions for two and three space dimensions.
Mathematics Subject Classification: 65M12 / 65M60
Key words: Nonlinear Schrödinger equation / two-step time discretization / linearly implicit method / finite element method / L2 and H1 error estimates / optimal order of convergence.
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