Error estimates of the Crank-Nicolson Galerkin method for the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge
Provides rigorous error analysis for a numerical method solving coupled Maxwell-Schrödinger equations, which is important for computational electromagnetics and quantum mechanics.
The paper presents a Crank-Nicolson finite element method for the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge and proves optimal error estimates via mathematical induction, confirmed by numerical examples.
In this paper we study the numerical method and the convergence for solving the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge. An alternating Crank-Nicolson finite element method for solving the problem is presented and the optimal error estimate for the numerical algorithm is obtained by a mathematical inductive method. Numerical examples are then carried out to confirm the theoretical results.