On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation
ESAIM: M2AN, 35 3 (2001) 389-405
Published online: 2002-04-15
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Optimal L2 error estimates of mass- and energy- conserved FE schemes for a nonlinear Schrödinger–type system
Zhuoyue Zhang and Wentao CaiJournal of Computational and Applied Mathematics 457 116313 (2025)
https://doi.org/10.1016/j.cam.2024.116313
Efficient numerical approximations for a nonconservative nonlinear Schrödinger equation appearing in wind‐forced ocean waves
Agissilaos Athanassoulis, Theodoros Katsaounis and Irene KyzaStudies in Applied Mathematics 153 (4) (2024)
https://doi.org/10.1111/sapm.12774
A novel multilevel finite element method for a generalized nonlinear Schrödinger equation
Fei Xu, Yasai Guo and Manting XieJournal of Computational and Applied Mathematics 116280 (2024)
https://doi.org/10.1016/j.cam.2024.116280
Uniform L∞-bounds for energy-conserving higher-order time integrators for the Gross–Pitaevskii equation with rotation
Christian Döding and Patrick HenningIMA Journal of Numerical Analysis 44 (5) 2892 (2024)
https://doi.org/10.1093/imanum/drad081
High-Order Mass- and Energy-Conserving Methods for the Nonlinear Schrödinger Equation
Genming Bai, Jiashun Hu and Buyang LiSIAM Journal on Scientific Computing 46 (2) A1026 (2024)
https://doi.org/10.1137/22M152178X
On the convergence of a linearly implicit finite element method for the nonlinear Schrödinger equation
Mohammad Asadzadeh and Georgios E. ZourarisStudies in Applied Mathematics (2024)
https://doi.org/10.1111/sapm.12743
A two level approach for simulating Bose–Einstein condensates by Localized Orthogonal Decomposition
Christian Döding, Patrick Henning, Johan Wärnegård, M. Picasso, A. Buffa, F. Nobile, S. Deparis, D. Kressner and J. HesthavenESAIM: Mathematical Modelling and Numerical Analysis 58 (6) 2317 (2024)
https://doi.org/10.1051/m2an/2024040
Unconditional optimal error estimates of a linearized mass- and energy- conservation FEM for a coupled nonlinear Schrödinger equations
Qinlong Li and Yu LiCommunications in Nonlinear Science and Numerical Simulation 124 107297 (2023)
https://doi.org/10.1016/j.cnsns.2023.107297
A novel, structure-preserving, second-order-in-time relaxation scheme for Schrödinger-Poisson systems
Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza and Stephen MetcalfeJournal of Computational Physics 490 112307 (2023)
https://doi.org/10.1016/j.jcp.2023.112307
Error Estimation of the Relaxation Finite Difference Scheme for the Nonlinear Schrödinger Equation
Georgios E. ZourarisSIAM Journal on Numerical Analysis 61 (1) 365 (2023)
https://doi.org/10.1137/21M1399130
Implicit-Explicit Finite Difference Approximations of a Semilinear Heat Equation with Logarithmic Nonlinearity
Panagiotis Paraschis and Georgios E. ZourarisComputational Methods in Applied Mathematics 23 (3) 695 (2023)
https://doi.org/10.1515/cmam-2022-0217
Unconditionally optimal error estimate of mass- and energy-stable Galerkin method for Schrödinger equation with cubic nonlinearity
Huaijun YangApplied Numerical Mathematics 183 39 (2023)
https://doi.org/10.1016/j.apnum.2022.08.016
Galerkin finite element method for damped nonlinear Schrödinger equation
Lingli Wang and Meng LiApplied Numerical Mathematics 178 216 (2022)
https://doi.org/10.1016/j.apnum.2022.03.018
A linearized compact ADI numerical method for the two-dimensional nonlinear delayed Schrödinger equation
Hongyu Qin, Fengyan Wu and Deng DingApplied Mathematics and Computation 412 126580 (2022)
https://doi.org/10.1016/j.amc.2021.126580
Error estimates of second-order BDF Galerkin finite element methods for a coupled nonlinear Schrödinger system
Yanhua Mei and Rong AnComputers & Mathematics with Applications 122 117 (2022)
https://doi.org/10.1016/j.camwa.2022.07.018
Iterative reconstruction algorithms for solving the Schrödinger equations on conical spaces
Joshua Warigue NdiayeAnalysis and Mathematical Physics 12 (1) (2022)
https://doi.org/10.1007/s13324-021-00645-7
Unconditional optimal error estimates of linearized backward Euler Galerkin FEMs for nonlinear Schrödinger-Helmholtz equations
Yun-Bo Yang and Yao-Lin JiangNumerical Algorithms 86 (4) 1495 (2021)
https://doi.org/10.1007/s11075-020-00942-5
Error estimation of the Besse Relaxation Scheme for a semilinear heat equation
Georgios E. ZourarisESAIM: Mathematical Modelling and Numerical Analysis 55 (1) 301 (2021)
https://doi.org/10.1051/m2an/2020077
Second-Order SAV Schemes for the Nonlinear Schrödinger Equation and Their Error Analysis
Beichuan Deng, Jie Shen and Qingqu ZhuangJournal of Scientific Computing 88 (3) (2021)
https://doi.org/10.1007/s10915-021-01576-y
A note on optimal $$H^1$$-error estimates for Crank-Nicolson approximations to the nonlinear Schrödinger equation
Patrick Henning and Johan WärnegårdBIT Numerical Mathematics 61 (1) 37 (2021)
https://doi.org/10.1007/s10543-020-00814-3
Structure-preserving Gauss methods for the nonlinear Schrödinger equation
Georgios Akrivis and Dongfang LiCalcolo 58 (2) (2021)
https://doi.org/10.1007/s10092-021-00405-w
Superconvergence of time invariants for the Gross–Pitaevskii equation
Patrick Henning and Johan WärnegårdMathematics of Computation 91 (334) 509 (2021)
https://doi.org/10.1090/mcom/3693
Nonconforming finite element method for a generalized nonlinear Schrödinger equation
Houchao Zhang, Dongyang Shi and Qingfu LiApplied Mathematics and Computation 377 125141 (2020)
https://doi.org/10.1016/j.amc.2020.125141
A Schrödinger-type algorithm for solving the Schrödinger equations via Phragmén–Lindelöf inequalities
Lingling ZhaoJournal of Inequalities and Applications 2019 (1) (2019)
https://doi.org/10.1186/s13660-019-2098-3
Unconditionally optimal error estimates of a new mixed FEM for nonlinear Schrödinger equations
Dongyang Shi and Huaijun YangAdvances in Computational Mathematics 45 (5-6) 3173 (2019)
https://doi.org/10.1007/s10444-019-09732-7
Approximating the Nonlinear Schrödinger Equation by a Two Level Linearly Implicit Finite Element Method
M. Asadzadeh and C. StandarJournal of Mathematical Sciences 239 (3) 233 (2019)
https://doi.org/10.1007/s10958-019-04301-1
Relay-Zone Technique for Numerical Boundary Treatments in Simulating Dark Solitons
Lei Bian and Shaoqiang TangMultiscale Science and Engineering 1 (3) 210 (2019)
https://doi.org/10.1007/s42493-018-00002-0
Superconvergence analysis of Crank‐Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation
Houchao Zhang and Junjun WangNumerical Methods for Partial Differential Equations 34 (2) 799 (2018)
https://doi.org/10.1002/num.22230
Low order nonconforming finite element method for time-dependent nonlinear Schrödinger equation
Chao Xu, Jiaquan Zhou, Dongyang Shi and Houchao ZhangBoundary Value Problems 2018 (1) (2018)
https://doi.org/10.1186/s13661-018-1093-9
Unconditional stability and convergence of Crank–Nicolson Galerkin FEMs for a nonlinear Schrödinger–Helmholtz system
Jilu WangNumerische Mathematik 139 (2) 479 (2018)
https://doi.org/10.1007/s00211-017-0944-0
Unconditional optimal error estimates for BDF2-FEM for a nonlinear Schrödinger equation
Wentao Cai, Jian Li and Zhangxin ChenJournal of Computational and Applied Mathematics 331 23 (2018)
https://doi.org/10.1016/j.cam.2017.09.010
A Linear Implicit Finite Difference Discretization of the Schrödinger–Hirota Equation
Georgios E. ZourarisJournal of Scientific Computing 77 (1) 634 (2018)
https://doi.org/10.1007/s10915-018-0718-6
A Posteriori Error Analysis for Evolution Nonlinear Schrödinger Equations up to the Critical Exponent
Theodoros Katsaounis and Irene KyzaSIAM Journal on Numerical Analysis 56 (3) 1405 (2018)
https://doi.org/10.1137/16M1108029
Crank–Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials
Patrick Henning and Daniel PeterseimMathematical Models and Methods in Applied Sciences 27 (11) 2147 (2017)
https://doi.org/10.1142/S0218202517500415
Optimal error analysis of Crank–Nicolson schemes for a coupled nonlinear Schrödinger system in 3D
Weiwei Sun and Jilu WangJournal of Computational and Applied Mathematics 317 685 (2017)
https://doi.org/10.1016/j.cam.2016.12.004
The Finite Element Method for the Time-Dependent Gross--Pitaevskii Equation with Angular Momentum Rotation
Patrick Henning and Axel MålqvistSIAM Journal on Numerical Analysis 55 (2) 923 (2017)
https://doi.org/10.1137/15M1009172
Unconditional convergence and optimal error estimates of the Euler semi-implicit scheme for a generalized nonlinear Schrödinger equation
Wentao Cai, Jian Li and Zhangxin ChenAdvances in Computational Mathematics 42 (6) 1311 (2016)
https://doi.org/10.1007/s10444-016-9463-2
Integrable discretization of nonlinear Schrödinger equation and its application with Fourier pseudo-spectral method
Y. Zhang, X. B. Hu and H. W. TamNumerical Algorithms 69 (4) 839 (2015)
https://doi.org/10.1007/s11075-014-9928-7
ANALYSIS OF A RELAXATION SCHEME FOR A NONLINEAR SCHRÖDINGER EQUATION OCCURRING IN PLASMA PHYSICS
Dietmar Oelz and Saber TrabelsiMathematical Modelling and Analysis 19 (2) 257 (2014)
https://doi.org/10.3846/13926292.2014.910279
A New Error Analysis of Crank–Nicolson Galerkin FEMs for a Generalized Nonlinear Schrödinger Equation
Jilu WangJournal of Scientific Computing 60 (2) 390 (2014)
https://doi.org/10.1007/s10915-013-9799-4
Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation
Weizhu Bao, Qinglin Tang and Zhiguo XuJournal of Computational Physics 235 423 (2013)
https://doi.org/10.1016/j.jcp.2012.10.054
Theory and numerical approximations for a nonlinear 1 + 1 Dirac system
Nikolaos Bournaveas and Georgios E. ZourarisESAIM: Mathematical Modelling and Numerical Analysis 46 (4) 841 (2012)
https://doi.org/10.1051/m2an/2011071
Trends in Industrial and Applied Mathematics
Graeme Fairweather and Morrakot KhebchareonApplied Optimization, Trends in Industrial and Applied Mathematics 72 219 (2002)
https://doi.org/10.1007/978-1-4613-0263-6_10