Energy and Mass Conservative Averaging Local Discontinuous Galerkin Method for Schrödinger Equation

Abstract

In this article, we develop the semi-discrete and fully discrete averaging local discontinuous Galerkin method to solve the well-known Schrödinger equation, in which space is discretized by the averaging local discontinuous Galerkin (ADG) method, and the time is discretized by Crank-Nicolson approach. Energy and mass conservative property of both schemes are proved. These schemes are shown to be unconditionally energy stable, and the error estimates are rigorously proved. Some numerical examples are performed to demonstrate the accuracy numerically.