Two-grid algorithm for two-dimensional linear Schrödinger equation by the mixed finite element method

Abstract

In this paper, we propose a new two-grid algorithm for solving two-dimensional Schrödinger equation in semi-discrete and fully discrete mixed finite element scheme, respectively. With this algorithm, the solution of the Schrödinger equation on a fine grid can be reduced to the original problem on a much coarser grid together with two Poisson equations on the fine grid. In addition, we obtain error results of the two-grid solution. At last, a numerical experiment is provided to demonstrate the efficiency of the two-grid algorithm.

Keywords

• Schrödinger equation
• Two-grid algorithm
• Mixed finite element method
• Backward Euler scheme