weak galerkin finite element method for the nonlinear schrodinger equation

The numerical technique for a two-dimensional time-dependent nonlinear schrodinger equation is the subject of this work. the approximations are produced using the weak galerkin finite element technique with semi-discrete and fully discrete finite element methods, respectively, using the backward euler method and the crank-nicolson method in time. using the elliptic projection operator, we provide optimum l² error estimates for semi and fully discrete weak galerkin finite elements. finally, we present numerical examples provided to verify our theoretical results.