TWO-GRID STRATEGY FOR UNSTEADY STATE NONLINEAR SCHRÖDINGER EQUATIONS

Abstract: Two-grid mixed finite element schemes are developed for solving 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. AMS Subject Classification: 35K57, 65M60 Key Words: nonlinear Schrödinger equations, two-grid methods, mixed finit