Numerical solution of two-dimensional nonlinear Schrödinger equation using a new two-grid finite element method

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2019.06.049 ◽

2020 ◽

Vol 364 ◽

pp. 112333 ◽

Author(s):

Hanzhang Hu ◽

Yanping Chen

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Numerical Solution ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger ◽

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Two-grid method for two-dimensional nonlinear Schrödinger equation by finite element method

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22193 ◽

2017 ◽

Vol 34 (2) ◽

pp. 385-400 ◽

Author(s):

Hanzhang Hu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Grid Method ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger ◽

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On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an:2001121 ◽

2001 ◽

Vol 35 (3) ◽

pp. 389-405 ◽

Author(s):

Georgios E. Zouraris

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

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A linearized energy–conservative finite element method for the nonlinear Schrödinger equation with wave operator

Applied Numerical Mathematics ◽

10.1016/j.apnum.2019.02.005 ◽

2019 ◽

Vol 140 ◽

pp. 183-198 ◽

Author(s):

Wentao Cai ◽

Dongdong He ◽

Kejia Pan

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

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Superconvergence analysis for nonlinear Schrödinger equation with two-grid finite element method

Applied Mathematics Letters ◽

10.1016/j.aml.2021.107553 ◽

2021 ◽

pp. 107553

Author(s):

Junjun Wang ◽

Meng Li ◽

Lijuan Guo

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

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Approximating the Nonlinear Schrödinger Equation by a Two Level Linearly Implicit Finite Element Method

Journal of Mathematical Sciences ◽

10.1007/s10958-019-04301-1 ◽

2019 ◽

Vol 239 (3) ◽

pp. 233-247

Author(s):

M. Asadzadeh ◽

C. Standar

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

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Superconvergence analysis of conforming finite element method for nonlinear Schrödinger equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2016.05.020 ◽

2016 ◽

Vol 289 ◽

pp. 298-310 ◽

Author(s):

Dongyang Shi ◽

Xin Liao ◽

Lele Wang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Conforming Finite Element ◽

Conforming Finite Element Method ◽

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A Two-Grid Finite-Element Method for the Nonlinear Schrödinger Equation

Journal of Computational Mathematics ◽

10.4208/jcm.1409-m4323 ◽

2015 ◽

Vol 33 (2) ◽

pp. 146-157 ◽

Author(s):

Jicheng Jin

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

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An energy-preserving Crank–Nicolson Galerkin spectral element method for the two dimensional nonlinear Schrödinger equation

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.05.025 ◽

2018 ◽

Vol 344 ◽

pp. 245-258 ◽

Author(s):

Haochen Li ◽

Zhenguo Mu ◽

Yushun Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Spectral Element Method ◽

Spectral Element ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger ◽

Element Method ◽

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An Efficient and Unconditionally Convergent Galerkin Finite Element Method for the Nonlinear Schrodinger Equation in High Dimensions

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.oa-2020-0033 ◽

2021 ◽

Vol 13 (4) ◽

pp. 735-760

Author(s):

global sci

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Galerkin Finite Element Method ◽

High Dimensions ◽

Galerkin Finite Element ◽

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Nonconforming finite element method for a generalized nonlinear Schrödinger equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2020.125141 ◽

2020 ◽

Vol 377 ◽

pp. 125141

Author(s):

Houchao Zhang ◽

Dongyang Shi ◽

Qingfu Li

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonconforming Finite Element ◽

Nonconforming Finite Element Method ◽

Generalized Nonlinear Schrödinger Equation ◽

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