A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method

Source abstract

The convergence of the discontinuous Galerkin method for the nonlinear (cubic) Schrödinger equation is analyzed in this paper. We show the existence of the resulting approximations and prove optimal order error estimates in L ∞ ( L 2 ) . L^{\infty }(L^{2} ) . These estimates are valid under weak restrictions on the space-time mesh.