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Chupeng Ma, Liqun Cao, Yanping Lin, Error estimates of Crank–Nicolson Galerkin method for the time-dependent Maxwell–Schrödinger equations under the Lorentz gauge, IMA Journal of Numerical Analysis, Volume 38, Issue 4, October 2018, Pages 2074–2104, https://doi.org/10.1093/imanum/drx060
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Abstract
In this article, we study a numerical method and its 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 an optimal error estimate for the numerical algorithm is obtained by a mathematical inductive method. Numerical experiments are then carried out to confirm the theoretical results.
© The authors 2017. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
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