Numerical solution of two-dimensional nonlinear Schrodinger equation using a new two-grid finite element method

摘要

A new two-grid finite element scheme is presented for two-dimensional nonlinear Schrodinger equation. One Newton iteration is applied on the fine grid to linearize the nonlinear system using the coarse-grid solution as the initial guess, and furthermore one more linear system on the coarse space is solved. The error estimations of the two-grid solution in the L-2 and H-1 norm are given. It is shown, both theoretically and numerically, that the coarse space can be extremely coarse and two-grid aliorithm still achieves optimal approximation as long as the mesh sizes satisfy H = O(h(1/3)).

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