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<p>In this paper, a linearized mass-preserving Galerkin finite element method is proposed to solve the multi-dimensional coupled nonlinear Schrödinger equations. The proof of an unconditional convergence is given without any time step restrictions. Our main idea is to obtain the boundedness of the numerical approximation in certain norms, where the Sobolev embedding theorem and the inverse inequality have been used. Numerical examples are given to demonstrate our theoretical results.</p>

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Optimal error estimates of the mass-preserving Galerkin finite element method for coupled nonlinear Schrödinger equations

  • 期刊论文

  • 发表日期：

    2026年7月20日

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  • Lili Li,
  • Wanqiu Yuan

摘要

In this paper, a linearized mass-preserving Galerkin finite element method is proposed to solve the multi-dimensional coupled nonlinear Schrödinger equations. The proof of an unconditional convergence is given without any time step restrictions. Our main idea is to obtain the boundedness of the numerical approximation in certain norms, where the Sobolev embedding theorem and the inverse inequality have been used. Numerical examples are given to demonstrate our theoretical results.