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linearly implicit method

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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On the convergence of a linear two-step finite element methodfor the nonlinear Schrödinger equation
Georgios E. Zouraris
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 35 / Issue 3 / May 2001

Published online by Cambridge University Press:

15 April 2002, pp. 389-405

Print publication:

May 2001
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We discretize the nonlinear Schrödinger equation,with Dirichlet boundary conditions, by a linearlyimplicit 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.