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 L-2 error estimates for semi and fully discrete weak Galerkin finite elements. Finally, we present numerical examples provided to verify our theoretical results.