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Two-grid mixed finite-element methods for nonlinear Schrödinger equations

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Abstract

Two-grid mixed finite element schemes are developed for solving both steady state and unsteady state nonlinear Schrödinger equations. The schemes use discretizations based on a mixed finite-element method. The two-grid approach yields iterative procedures for solving the nonlinear discrete equations. The idea is to relegate all of the Newton-like iterations to grids much coarser than the final one, with no loss in order of accuracy. Numerical tests are performed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 63-73, 2012

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