An efficient finite element method for the two-dimensional nonlinear time–space fractional Schrödinger equation on an irregular convex domain

Applied Mathematics Letters ◽

10.1016/j.aml.2018.06.028 ◽

2018 ◽

Vol 86 ◽

pp. 103-110 ◽

Author(s):

Wenping Fan ◽

Haitao Qi

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Convex Domain ◽

Schrodinger Equation ◽

Two Dimensional ◽

Fractional Schrödinger Equation ◽

Fractional Schrodinger Equation ◽

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Error analysis of the unstructured mesh finite element method for the two-dimensional time-space fractional Schrödinger equation with a time-independent potential

International Journal of Computer Mathematics ◽

10.1080/00207160.2020.1846726 ◽

2020 ◽

pp. 1-20

Author(s):

Wenping Fan ◽

Xiaoyun Jiang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Error Analysis ◽

Schrodinger Equation ◽

Unstructured Mesh ◽

Two Dimensional ◽

Fractional Schrodinger Equation ◽

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The inverse problem and the second order θ scheme with finite element method used for 2D nonlinear space fractional Schrödinger equation

Applied Mathematics Letters ◽

10.1016/j.aml.2019.06.013 ◽

2019 ◽

Vol 98 ◽

pp. 240-247

Author(s):

Wenping Fan ◽

Hui Zhang

Keyword(s):

Finite Element Method ◽

Inverse Problem ◽

Finite Element ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Second Order ◽

Fractional Schrödinger Equation ◽

Fractional Schrodinger Equation ◽

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A fast energy conserving finite element method for the nonlinear fractional Schrödinger equation with wave operator

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.06.010 ◽

2018 ◽

Vol 338 ◽

pp. 758-773 ◽

Author(s):

Meng Li ◽

Yong-Liang Zhao

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Fractional Schrödinger Equation ◽

Energy Conserving ◽

Nonlinear Fractional Schrödinger Equation ◽

Fractional Schrodinger Equation ◽

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

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2017.10.018 ◽

2018 ◽

Vol 75 (3) ◽

pp. 900-917 ◽

Author(s):

Hanzhang Hu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Mixed Finite Element ◽

Grid Method ◽

Mixed Finite Element Method ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

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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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Two-grid method for the two-dimensional time-dependent Schrödinger equation by the finite element method

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2019.01.030 ◽

2019 ◽

Vol 77 (12) ◽

pp. 3043-3053

Author(s):

Zhikun Tian ◽

Yanping Chen ◽

Yunqing Huang ◽

Jianyun Wang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Grid Method ◽

Time Dependent ◽

Two Dimensional ◽

The Finite Element Method ◽

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A two-dimensional multilevel adaptive finite element method for the time-independent Schrödinger equation

Chemical Physics Letters ◽

10.1016/0009-2614(93)85463-x ◽

1993 ◽

Vol 214 (1) ◽

pp. 109-117 ◽

Author(s):

J. Ackermann ◽

R. Roitzsch

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Adaptive Finite Element Method ◽

Adaptive Finite Element ◽

Two Dimensional ◽

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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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Promotion of the proton transfer reaction by the intermolecular stretching mode: Application of the two‐dimensional finite element method to the nuclear Schrödinger equation

The Journal of Chemical Physics ◽

10.1063/1.454998 ◽

1988 ◽

Vol 89 (5) ◽

pp. 2932-2937 ◽

Author(s):

Nobuyuki Sato ◽

Suehiro Iwata

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Proton Transfer ◽

Schrodinger Equation ◽

Transfer Reaction ◽

Proton Transfer Reaction ◽

Two Dimensional ◽

Dimensional Finite Element ◽

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Application of finite-element method to the two-dimensional Schrödinger equation

Journal of Computational Chemistry ◽

10.1002/jcc.540090306 ◽

1988 ◽

Vol 9 (3) ◽

pp. 222-231 ◽

Author(s):

Nobuyuki Sato ◽

Suehiro Iwata

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Two Dimensional ◽

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