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.

Received: February 25, 2011

AMS Subject Classification: 35K57, 65M60

Key Words and Phrases: nonlinear Schrödinger equations, two-grid methods, mixed finite element methods, coupled systems

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 68
Issue: 4