Convergence of a Strang splitting finite element discretization for the Schrödinger–Poisson equation
Convergence of a Strang splitting finite element discretization for the Schrödinger–Poisson equation
Operator splitting methods combined with finite element spatial discretizations are studied for time-dependent nonlinear Schrödinger equations. In particular, the Schrödinger–Poisson equation under homogeneous Dirichlet boundary conditions on a finite domain is considered. A rigorous stability and error analysis is carried out for the second-order Strang splitting method and conforming polynomial …