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Unconditionally optimal error estimates of a new mixed FEM for nonlinear Schrödinger equations

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Abstract

In this paper, a new mixed finite element scheme in space and a linearized backward Euler scheme in time are presented and investigated for the nonlinear Schrödinger equations. By introducing a suitable time-discrete system, both the errors in L2- and H1-norms for the original variable and L2-norm for the flux variable are derived without any time-step restriction, while previous works always required certain conditions between time step and space size. Finally, some numerical results are provided to verify the theoretical analysis.

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Funding

This work is supported by the National Natural Science Foundation of China (Nos. 11671369; 11271340).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, People’s Republic of China

    Dongyang Shi & Huaijun Yang

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  1. Dongyang Shi
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  2. Huaijun Yang
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Correspondence to Dongyang Shi.

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Communicated by: Long Chen

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Shi, D., Yang, H. Unconditionally optimal error estimates of a new mixed FEM for nonlinear Schrödinger equations. Adv Comput Math 45, 3173–3194 (2019). https://doi.org/10.1007/s10444-019-09732-7

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  • DOI: https://doi.org/10.1007/s10444-019-09732-7

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