A Space-Time Finite Element Method for the Nonlinear Schrödinger Equation: The Continuous Galerkin Method

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142997330111 ◽

1999 ◽

Vol 36 (6) ◽

pp. 1779-1807 ◽

Author(s):

Ohannes Karakashian ◽

Charalambos Makridakis

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Galerkin Method ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Continuous Galerkin ◽

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A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method

Mathematics of Computation ◽

10.1090/s0025-5718-98-00946-6 ◽

1998 ◽

Vol 67 (222) ◽

pp. 479-500 ◽

Author(s):

Ohannes Karakashian ◽

Charalambos Makridakis

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

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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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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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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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A quadratic B-spline finite element method for solving nonlinear Schrödinger equation

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/s0045-7825(98)00257-6 ◽

1999 ◽

Vol 174 (1-2) ◽

pp. 247-258 ◽

Author(s):

. Da

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

B Spline ◽

Spline Finite Element ◽

Element Method ◽

Spline Finite Element Method

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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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A quintic B-spline finite-element method for solving the nonlinear Schrödinger equation

Physics of Wave Phenomena ◽

10.3103/s1541308x12020033 ◽

2012 ◽

Vol 20 (2) ◽

pp. 107-117 ◽

Author(s):

B. Saka

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

B Spline ◽

Spline Finite Element ◽

Element Method ◽

Spline Finite Element Method

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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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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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