Unconditionally optimal error estimates of a new mixed FEM for nonlinear Schrodinger equations

摘要

In this paper, a new mixed finite element scheme in space and a linearized backward Euler scheme in time are presented and investigated for the nonlinear Schrodinger equations. By introducing a suitable time-discrete system, both the errors in L-2- and H-1-norms for the original variable and L-2-norm for the flux variable are derived without any time-step restriction, while previous works always required certain conditions between time step and space size. Finally, some numerical results are provided to verify the theoretical analysis.