Bai, Genming; Hu, Jiashun; Li, Buyang High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation. (English) Zbl 07820571 SIAM J. Sci. Comput. 46, No. 2, A1026-A1046 (2024). MSC: 65M70 65N30 65H10 65M12 65M15 35Q55 35Q41 81Q05 PDFBibTeX XMLCite \textit{G. Bai} et al., SIAM J. Sci. Comput. 46, No. 2, A1026--A1046 (2024; Zbl 07820571) Full Text: DOI
Li, Meng; Zhao, Jikun; Chen, Shaochun Unconditional error analysis of VEMs for a generalized nonlinear Schrödinger equation. (English) Zbl 07806682 J. Comput. Math. 42, No. 2, 500-543 (2024). MSC: 65N35 65N12 76D07 65N15 PDFBibTeX XMLCite \textit{M. Li} et al., J. Comput. Math. 42, No. 2, 500--543 (2024; Zbl 07806682) Full Text: DOI
Li, Meng; Zhao, Jikun; Wang, Zhongchi; Chen, Shaochun Conservative conforming and nonconforming vems for fourth order nonlinear Schrödinger equations with trapped term. (English) Zbl 07806681 J. Comput. Math. 42, No. 2, 454-499 (2024). MSC: 65N35 65N12 76D07 65N15 PDFBibTeX XMLCite \textit{M. Li} et al., J. Comput. Math. 42, No. 2, 454--499 (2024; Zbl 07806681) Full Text: DOI
Wang, Lingli; Li, Meng; Peng, Shanshan Conservative \(EQ_1^{rot}\) nonconforming FEM for nonlinear Schrödinger equation with wave operator. (English) Zbl 07798409 Numer. Methods Partial Differ. Equations 40, No. 1, Article ID e23057, 24 p. (2024). MSC: 65M60 65M06 PDFBibTeX XMLCite \textit{L. Wang} et al., Numer. Methods Partial Differ. Equations 40, No. 1, Article ID e23057, 24 p. (2024; Zbl 07798409) Full Text: DOI
Wang, Li-Lian; Yan, Jingye; Zhang, Xiaolong Error analysis of a first-order IMEX scheme for the logarithmic Schrödinger equation. (English) Zbl 07794525 SIAM J. Numer. Anal. 62, No. 1, 119-137 (2024). MSC: 65N35 65N22 65F05 65N15 35J05 35B65 35Q55 35Q41 PDFBibTeX XMLCite \textit{L.-L. Wang} et al., SIAM J. Numer. Anal. 62, No. 1, 119--137 (2024; Zbl 07794525) Full Text: DOI arXiv
Bao, Weizhu; Wang, Chushan Optimal error bounds on the exponential wave integrator for the nonlinear Schrödinger equation with low regularity potential and nonlinearity. (English) Zbl 07794524 SIAM J. Numer. Anal. 62, No. 1, 93-118 (2024). MSC: 35Q55 35Q41 35S30 81Q05 65M70 65M15 35B65 PDFBibTeX XMLCite \textit{W. Bao} and \textit{C. Wang}, SIAM J. Numer. Anal. 62, No. 1, 93--118 (2024; Zbl 07794524) Full Text: DOI arXiv
Shi, Dongyang; Qi, Zhenqi Unconditional superconvergence analysis of an energy-preserving finite element scheme for nonlinear BBM equation. (English) Zbl 07784334 Comput. Math. Appl. 153, 172-185 (2024). MSC: 65M60 65M12 65N30 65M06 35Q53 PDFBibTeX XMLCite \textit{D. Shi} and \textit{Z. Qi}, Comput. Math. Appl. 153, 172--185 (2024; Zbl 07784334) Full Text: DOI
Shi, Dongyang; Zhang, Lingen Unconditional superconvergence analysis of modified finite difference streamlined diffusion method for nonlinear convection-dominated diffusion equation. (English) Zbl 07784328 Comput. Math. Appl. 153, 81-93 (2024). MSC: 65N30 65M15 65M60 65M06 65M12 PDFBibTeX XMLCite \textit{D. Shi} and \textit{L. Zhang}, Comput. Math. Appl. 153, 81--93 (2024; Zbl 07784328) Full Text: DOI
Qian, Xu; Zhang, Hong; Yan, Jingye; Song, Songhe Novel high-order mass- and energy-conservative Runge-Kutta integrators for the regularized logarithmic Schrödinger equation. (English) Zbl 07814774 Numer. Math., Theory Methods Appl. 16, No. 4, 993-1012 (2023). MSC: 35Q55 65L06 81Q05 PDFBibTeX XMLCite \textit{X. Qian} et al., Numer. Math., Theory Methods Appl. 16, No. 4, 993--1012 (2023; Zbl 07814774) Full Text: DOI
Shi, Dongyang; Zhang, Houchao Superconvergence analysis of a conservative mixed finite element method for the nonlinear Klein-Gordon-Schrödinger equations. (English) Zbl 07777340 Numer. Methods Partial Differ. Equations 39, No. 4, 2909-2934 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{D. Shi} and \textit{H. Zhang}, Numer. Methods Partial Differ. Equations 39, No. 4, 2909--2934 (2023; Zbl 07777340) Full Text: DOI
Hu, Hanzhang \(L^p\) error estimate of nonlinear Schrödinger equation using a two-grid finite element method. (English) Zbl 07777338 Numer. Methods Partial Differ. Equations 39, No. 4, 2865-2884 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{H. Hu}, Numer. Methods Partial Differ. Equations 39, No. 4, 2865--2884 (2023; Zbl 07777338) Full Text: DOI
Ma, Shu; Wang, Jilu; Zhang, Mingyan; Zhang, Zhimin Mass- and energy-conserving Gauss collocation methods for the nonlinear Schrödinger equation with a wave operator. (English) Zbl 07773316 Adv. Comput. Math. 49, No. 6, Paper No. 77, 38 p. (2023). Reviewer: Dana Černá (Liberec) MSC: 65M60 65M70 65H10 65H10 65M15 65M12 35Q55 35Q41 PDFBibTeX XMLCite \textit{S. Ma} et al., Adv. Comput. Math. 49, No. 6, Paper No. 77, 38 p. (2023; Zbl 07773316) Full Text: DOI
Li, Dongfang; Li, Xiaoxi; Sun, Hai-wei Optimal error estimates of SAV Crank-Nicolson finite element method for the coupled nonlinear Schrödinger equation. (English) Zbl 07766141 J. Sci. Comput. 97, No. 3, Paper No. 71, 26 p. (2023). MSC: 65F35 15A12 15A18 PDFBibTeX XMLCite \textit{D. Li} et al., J. Sci. Comput. 97, No. 3, Paper No. 71, 26 p. (2023; Zbl 07766141) Full Text: DOI
Shi, Dongyang; Qi, Zhenqi Unconditional superconvergence analysis of an energy conservation scheme with Galerkin FEM for nonlinear Benjamin-Bona-Mahony equation. (English) Zbl 07759149 Commun. Nonlinear Sci. Numer. Simul. 127, Article ID 107572, 16 p. (2023). MSC: 65Mxx PDFBibTeX XMLCite \textit{D. Shi} and \textit{Z. Qi}, Commun. Nonlinear Sci. Numer. Simul. 127, Article ID 107572, 16 p. (2023; Zbl 07759149) Full Text: DOI
Shi, Dongyang; Ma, He Unconditional superconvergence analysis of a modified nonconforming energy stable BDF2 FEM for Sobolev equations with Burgers’ type nonlinearity. (English) Zbl 07758892 Commun. Nonlinear Sci. Numer. Simul. 126, Article ID 107440, 12 p. (2023). MSC: 65-XX PDFBibTeX XMLCite \textit{D. Shi} and \textit{H. Ma}, Commun. Nonlinear Sci. Numer. Simul. 126, Article ID 107440, 12 p. (2023; Zbl 07758892) Full Text: DOI
Liang, Conggang Superconvergence analysis for nonlinear viscoelastic wave equation with strong damping. (English) Zbl 1520.65068 Appl. Anal. 102, No. 12, 3489-3502 (2023). MSC: 65M60 65M12 65M15 PDFBibTeX XMLCite \textit{C. Liang}, Appl. Anal. 102, No. 12, 3489--3502 (2023; Zbl 1520.65068) Full Text: DOI
Wang, Dan; Li, Meng; Lu, Yu Unconditionally convergent and superconvergent analysis of second-order weighted IMEX FEMs for nonlinear Ginzburg-Landau equation. (English) Zbl 07741326 Comput. Math. Appl. 146, 84-105 (2023). MSC: 65M60 65M12 65M15 65M06 35Q56 PDFBibTeX XMLCite \textit{D. Wang} et al., Comput. Math. Appl. 146, 84--105 (2023; Zbl 07741326) Full Text: DOI
Chen, Fang; Li, Meng; Zhao, Yanmin; Tang, Yifa Convergence and superconvergence analysis of finite element methods for nonlinear Ginzburg-Landau equation with Caputo derivative. (English) Zbl 07735387 Comput. Appl. Math. 42, No. 6, Paper No. 271, 32 p. (2023). MSC: 65L60 65N30 PDFBibTeX XMLCite \textit{F. Chen} et al., Comput. Appl. Math. 42, No. 6, Paper No. 271, 32 p. (2023; Zbl 07735387) Full Text: DOI
Yang, Huaijun Unconditionally optimal error estimate of the Crank-Nicolson extrapolation Galerkin finite element method for Kuramoto-Tsuzuki equation. (English) Zbl 07735375 Comput. Appl. Math. 42, No. 6, Paper No. 259, 20 p. (2023). MSC: 65M15 65M60 65N15 65N30 PDFBibTeX XMLCite \textit{H. Yang}, Comput. Appl. Math. 42, No. 6, Paper No. 259, 20 p. (2023; Zbl 07735375) Full Text: DOI
Yang, Huaijun A new error analysis of backward Euler Galerkin finite element method for two-dimensional time-dependent Ginzburg-Landau equation. (English) Zbl 07727135 Appl. Math. Lett. 145, Article ID 108767, 8 p. (2023). MSC: 65Mxx 35Qxx 65Nxx PDFBibTeX XMLCite \textit{H. Yang}, Appl. Math. Lett. 145, Article ID 108767, 8 p. (2023; Zbl 07727135) Full Text: DOI
Liu, Huini; Yi, Nianyu Optimal a priori error estimate of relaxation-type linear finite element method for nonlinear Schrödinger equation. (English) Zbl 1516.65090 J. Comput. Appl. Math. 428, Article ID 115147, 24 p. (2023). MSC: 65M60 35Q55 65M15 PDFBibTeX XMLCite \textit{H. Liu} and \textit{N. Yi}, J. Comput. Appl. Math. 428, Article ID 115147, 24 p. (2023; Zbl 1516.65090) Full Text: DOI
Yang, Huaijun; Shi, Dongyang Unconditionally superconvergent error estimates of a linearized Galerkin finite element method for the nonlinear thermistor problem. (English) Zbl 07709692 Adv. Comput. Math. 49, No. 3, Paper No. 33, 27 p. (2023). MSC: 65Mxx PDFBibTeX XMLCite \textit{H. Yang} and \textit{D. Shi}, Adv. Comput. Math. 49, No. 3, Paper No. 33, 27 p. (2023; Zbl 07709692) Full Text: DOI
Yang, Huaijun; Shi, Dongyang A novel approach of unconditional optimal error estimate of linearized and conservative Galerkin FEM for Klein-Gordon-Schrödinger equations. (English) Zbl 07693651 Commun. Nonlinear Sci. Numer. Simul. 123, Article ID 107286, 18 p. (2023). MSC: 65-XX 93-XX 34-XX PDFBibTeX XMLCite \textit{H. Yang} and \textit{D. Shi}, Commun. Nonlinear Sci. Numer. Simul. 123, Article ID 107286, 18 p. (2023; Zbl 07693651) Full Text: DOI
Wang, Jialing; Wang, Tingchun; Wang, Yushun A new framework of convergence analysis for solving the general nonlinear Schrödinger equation using the Fourier pseudo-spectral method in two dimensions. (English) Zbl 07679220 Adv. Appl. Math. Mech. 15, No. 3, 786-813 (2023). MSC: 65Mxx 35Q55 65T50 PDFBibTeX XMLCite \textit{J. Wang} et al., Adv. Appl. Math. Mech. 15, No. 3, 786--813 (2023; Zbl 07679220) Full Text: DOI
Shi, Dongyang; Zhang, Houchao Unconditional error estimates of linearized BDF2-Galerkin FEMs for nonlinear coupled Schrödinger-Helmholtz equations. (English) Zbl 07676498 Numer. Algorithms 92, No. 3, 1679-1705 (2023). MSC: 65M60 65M06 65N30 65M12 65N15 35Q60 35Q55 35Q41 PDFBibTeX XMLCite \textit{D. Shi} and \textit{H. Zhang}, Numer. Algorithms 92, No. 3, 1679--1705 (2023; Zbl 07676498) Full Text: DOI
Zouraris, Georgios E. Error estimation of the relaxation finite difference scheme for the nonlinear Schrödinger equation. (English) Zbl 07670868 SIAM J. Numer. Anal. 61, No. 1, 365-397 (2023). MSC: 65M06 65N06 65M12 65M15 35Q55 35Q41 PDFBibTeX XMLCite \textit{G. E. Zouraris}, SIAM J. Numer. Anal. 61, No. 1, 365--397 (2023; Zbl 07670868) Full Text: DOI arXiv
Li, Yuan; Cui, Xuewei Unconditionally optimal error analysis of the second-order BDF finite element method for the Kuramoto-Tsuzuki equation. (English) Zbl 1515.65296 J. Comput. Math. 41, No. 2, 211-223 (2023). MSC: 65N30 65N12 65N15 PDFBibTeX XMLCite \textit{Y. Li} and \textit{X. Cui}, J. Comput. Math. 41, No. 2, 211--223 (2023; Zbl 1515.65296) Full Text: DOI
Yang, Huaijun; Wang, Lele; Liao, Xin Superconvergence analysis of a linearized energy-conservative Galerkin method for the nonlinear Schrödinger equation with wave operator. (English) Zbl 07654111 Comput. Math. Appl. 133, 142-154 (2023). MSC: 35Q55 65M60 65M12 65M06 65M15 PDFBibTeX XMLCite \textit{H. Yang} et al., Comput. Math. Appl. 133, 142--154 (2023; Zbl 07654111) Full Text: DOI
Liu, Jianfeng; Wang, Tingchun; Zhang, Teng A second-order finite difference scheme for the multi-dimensional nonlinear time-fractional Schrödinger equation. (English) Zbl 1506.65127 Numer. Algorithms 92, No. 2, 1153-1182 (2023). MSC: 65M06 65N06 65M12 65M15 35R11 35Q41 35Q55 PDFBibTeX XMLCite \textit{J. Liu} et al., Numer. Algorithms 92, No. 2, 1153--1182 (2023; Zbl 1506.65127) Full Text: DOI
Yi, Huaming; Chen, Yanping; Wang, Yang; Huang, Yunqing Optimal convergence analysis of a linearized second-order BDF-PPIFE method for semi-linear parabolic interface problems. (English) Zbl 1510.65286 Appl. Math. Comput. 438, Article ID 127581, 20 p. (2023). MSC: 65N15 35R05 65N30 PDFBibTeX XMLCite \textit{H. Yi} et al., Appl. Math. Comput. 438, Article ID 127581, 20 p. (2023; Zbl 1510.65286) Full Text: DOI
Yang, Huaijun Unconditionally optimal error estimate of mass- and energy-stable Galerkin method for Schrödinger equation with cubic nonlinearity. (English) Zbl 1500.65074 Appl. Numer. Math. 183, 39-55 (2023). MSC: 65M60 65M06 65N30 65M15 35Q55 35Q41 PDFBibTeX XMLCite \textit{H. Yang}, Appl. Numer. Math. 183, 39--55 (2023; Zbl 1500.65074) Full Text: DOI
Li, Meng Cut-off error splitting technique for conservative nonconforming VEM for \(N\)-coupled nonlinear Schrödinger-Boussinesq equations. (English) Zbl 1504.65208 J. Sci. Comput. 93, No. 3, Paper No. 86, 44 p. (2022). MSC: 65M60 65M06 65N30 65N35 65N12 65N15 76D07 35Q35 35Q55 35Q41 PDFBibTeX XMLCite \textit{M. Li}, J. Sci. Comput. 93, No. 3, Paper No. 86, 44 p. (2022; Zbl 1504.65208) Full Text: DOI
Shi, Dongyang; Zhang, Houchao Unconditional optimal error estimates and superconvergence analysis of energy-preserving FEM for general nonlinear Schrödinger equation with wave operator. (English) Zbl 1504.65213 Comput. Math. Appl. 128, 79-95 (2022). MSC: 65M60 35Q55 65M15 PDFBibTeX XMLCite \textit{D. Shi} and \textit{H. Zhang}, Comput. Math. Appl. 128, 79--95 (2022; Zbl 1504.65213) Full Text: DOI
Mei, Yanhua; An, Rong Error estimates of second-order BDF Galerkin finite element methods for a coupled nonlinear Schrödinger system. (English) Zbl 1524.65578 Comput. Math. Appl. 122, 117-125 (2022). MSC: 65M60 35Q55 65M12 65M06 65M15 65B05 35Q41 65N30 PDFBibTeX XMLCite \textit{Y. Mei} and \textit{R. An}, Comput. Math. Appl. 122, 117--125 (2022; Zbl 1524.65578) Full Text: DOI
Zhang, Houchao; Zhu, Weijun Superconvergence analysis of a nonconforming MFEM for nonlinear Schrödinger equation. (English) Zbl 1497.65187 Appl. Anal. 101, No. 14, 4942-4964 (2022). MSC: 65M60 65M06 65N30 65N15 65N12 35A01 35A02 35Q55 35Q41 PDFBibTeX XMLCite \textit{H. Zhang} and \textit{W. Zhu}, Appl. Anal. 101, No. 14, 4942--4964 (2022; Zbl 1497.65187) Full Text: DOI
Hu, Hanzhang; Li, Buyang; Zou, Jun Optimal convergence of the Newton iterative Crank-Nicolson finite element method for the nonlinear Schrödinger equation. (English) Zbl 1492.65265 Comput. Methods Appl. Math. 22, No. 3, 591-612 (2022). MSC: 65M60 35Q55 65M12 65M15 PDFBibTeX XMLCite \textit{H. Hu} et al., Comput. Methods Appl. Math. 22, No. 3, 591--612 (2022; Zbl 1492.65265) Full Text: DOI
Wang, Junjun; Li, Meng Superconvergence results for nonlinear Klein-Gordon-Schrödinger equation with backward differential formula finite element method. (English) Zbl 1524.65606 Comput. Math. Appl. 118, 214-229 (2022). MSC: 65M60 65M15 65M12 65M06 35Q55 35Q41 65N30 PDFBibTeX XMLCite \textit{J. Wang} and \textit{M. Li}, Comput. Math. Appl. 118, 214--229 (2022; Zbl 1524.65606) Full Text: DOI
Xu, Chao; Pei, Lifang Unconditional optimal error estimates of a modified finite element fully discrete scheme for the complex Ginzburg-Landau equation. (English) Zbl 1524.65615 Comput. Math. Appl. 115, 1-13 (2022). MSC: 65M60 65M12 65M06 35Q56 65M15 PDFBibTeX XMLCite \textit{C. Xu} and \textit{L. Pei}, Comput. Math. Appl. 115, 1--13 (2022; Zbl 1524.65615) Full Text: DOI
Wang, Lingli; Li, Meng Galerkin finite element method for damped nonlinear Schrödinger equation. (English) Zbl 1496.65173 Appl. Numer. Math. 178, 216-247 (2022). MSC: 65M60 65M06 65N30 65M15 35Q55 35Q41 PDFBibTeX XMLCite \textit{L. Wang} and \textit{M. Li}, Appl. Numer. Math. 178, 216--247 (2022; Zbl 1496.65173) Full Text: DOI
Wang, Jianyun; Tian, Zhikun Superconvergence of finite element approximations of the two-dimensional cubic nonlinear Schrödinger equation. (English) Zbl 1499.65686 Adv. Appl. Math. Mech. 14, No. 3, 652-665 (2022). MSC: 65N30 65N15 65N12 35Q55 PDFBibTeX XMLCite \textit{J. Wang} and \textit{Z. Tian}, Adv. Appl. Math. Mech. 14, No. 3, 652--665 (2022; Zbl 1499.65686) Full Text: DOI
Feng, Xiaobing; Ma, Shu Stable numerical methods for a stochastic nonlinear Schrödinger equation with linear multiplicative noise. (English) Zbl 1484.65216 Discrete Contin. Dyn. Syst., Ser. S 15, No. 4, 687-711 (2022). MSC: 65M60 35Q55 35Q60 65M12 PDFBibTeX XMLCite \textit{X. Feng} and \textit{S. Ma}, Discrete Contin. Dyn. Syst., Ser. S 15, No. 4, 687--711 (2022; Zbl 1484.65216) Full Text: DOI
Li, Minghao; Li, Zhenzhen; Shi, Dongyang Unconditional optimal error estimates for the transient Navier-Stokes equations with damping. (English) Zbl 1499.65502 Adv. Appl. Math. Mech. 14, No. 1, 248-274 (2022). MSC: 65M60 PDFBibTeX XMLCite \textit{M. Li} et al., Adv. Appl. Math. Mech. 14, No. 1, 248--274 (2022; Zbl 1499.65502) Full Text: DOI
Henning, Patrick; Wärnegård, Johan Superconvergence of time invariants for the Gross-Pitaevskii equation. (English) Zbl 1483.35213 Math. Comput. 91, No. 334, 509-555 (2022). MSC: 35Q55 65M60 65M06 65N30 65M12 65M15 81Q05 PDFBibTeX XMLCite \textit{P. Henning} and \textit{J. Wärnegård}, Math. Comput. 91, No. 334, 509--555 (2022; Zbl 1483.35213) Full Text: DOI arXiv
Shi, Dongyang; Zhang, Houchao A linearized conservative nonconforming FEM for nonlinear Klein-Gordon-Schrödinger equations. (English) Zbl 1524.65594 Comput. Math. Appl. 106, 57-73 (2022). MSC: 65M60 35Q55 65M12 65M15 65N30 35Q41 65M06 65Y05 PDFBibTeX XMLCite \textit{D. Shi} and \textit{H. Zhang}, Comput. Math. Appl. 106, 57--73 (2022; Zbl 1524.65594) Full Text: DOI
Wang, Junjun; Li, Meng; Zhang, Yu Superconvergence analysis of BDF-Galerkin FEM for nonlinear Schrödinger equation. (English) Zbl 07456974 Numer. Algorithms 89, No. 1, 195-222 (2022). MSC: 65Mxx PDFBibTeX XMLCite \textit{J. Wang} et al., Numer. Algorithms 89, No. 1, 195--222 (2022; Zbl 07456974) Full Text: DOI
Li, Yuan; An, Rong Unconditionally optimal error analysis of a linear Euler FEM scheme for the Navier-Stokes equations with mass diffusion. (English) Zbl 1481.35337 J. Sci. Comput. 90, No. 1, Paper No. 47, 31 p. (2022). MSC: 35Q35 76D05 65M60 65M06 65N30 65M12 65M15 PDFBibTeX XMLCite \textit{Y. Li} and \textit{R. An}, J. Sci. Comput. 90, No. 1, Paper No. 47, 31 p. (2022; Zbl 1481.35337) Full Text: DOI
Li, Meng; Wei, Yifan; Niu, Binqian; Zhao, Yong-Liang Fast L2-1\(_\sigma\) Galerkin FEMs for generalized nonlinear coupled Schrödinger equations with Caputo derivatives. (English) Zbl 1510.65247 Appl. Math. Comput. 416, Article ID 126734, 22 p. (2022). MSC: 65M60 35Q55 PDFBibTeX XMLCite \textit{M. Li} et al., Appl. Math. Comput. 416, Article ID 126734, 22 p. (2022; Zbl 1510.65247) Full Text: DOI
Guan, Zhen; Wang, Jungang; Liu, Ying; Nie, Yufeng Unconditionally optimal convergence of a linearized Galerkin FEM for the nonlinear time-fractional mobile/immobile transport equation. (English) Zbl 1484.65220 Appl. Numer. Math. 172, 133-156 (2022). MSC: 65M60 35R11 65M12 65M15 PDFBibTeX XMLCite \textit{Z. Guan} et al., Appl. Numer. Math. 172, 133--156 (2022; Zbl 1484.65220) Full Text: DOI
Li, Shan; Wang, Tingchun; Wang, Jialing; Guo, Boling An efficient and accurate Fourier pseudo-spectral method for the nonlinear Schrödinger equation with wave operator. (English) Zbl 1480.65285 Int. J. Comput. Math. 98, No. 2, 340-356 (2021). MSC: 65M70 65M06 35Q55 65M12 65M15 PDFBibTeX XMLCite \textit{S. Li} et al., Int. J. Comput. Math. 98, No. 2, 340--356 (2021; Zbl 1480.65285) Full Text: DOI
Li, Buyang; Wu, Yifei A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation. (English) Zbl 1481.65174 Numer. Math. 149, No. 1, 151-183 (2021). MSC: 65M22 65T50 65M12 65M15 35Q55 35Q41 PDFBibTeX XMLCite \textit{B. Li} and \textit{Y. Wu}, Numer. Math. 149, No. 1, 151--183 (2021; Zbl 1481.65174) Full Text: DOI arXiv
Li, Meng; Zhao, Jikun; Wang, Nan; Chen, Shaochun Conforming and nonconforming conservative virtual element methods for nonlinear Schrödinger equation: a unified framework. (English) Zbl 1506.65156 Comput. Methods Appl. Mech. Eng. 380, Article ID 113793, 27 p. (2021). MSC: 65M60 35Q55 65M12 PDFBibTeX XMLCite \textit{M. Li} et al., Comput. Methods Appl. Mech. Eng. 380, Article ID 113793, 27 p. (2021; Zbl 1506.65156) Full Text: DOI
Wang, Junjun; Li, Meng; Guo, Lijuan Superconvergence analysis for nonlinear Schrödinger equation with two-grid finite element method. (English) Zbl 1524.35606 Appl. Math. Lett. 122, Article ID 107553, 9 p. (2021). MSC: 35Q55 65M12 65M15 65M60 65M06 PDFBibTeX XMLCite \textit{J. Wang} et al., Appl. Math. Lett. 122, Article ID 107553, 9 p. (2021; Zbl 1524.35606) Full Text: DOI
Cheng, Yue; Wang, Tingchun; Guo, Boling An efficient and unconditionally convergent Galerkin finite element method for the nonlinear Schrödinger equation in high dimensions. (English) Zbl 1488.65412 Adv. Appl. Math. Mech. 13, No. 4, 735-760 (2021). MSC: 65M60 35Q55 35Q41 41A58 65N30 65M12 65M15 PDFBibTeX XMLCite \textit{Y. Cheng} et al., Adv. Appl. Math. Mech. 13, No. 4, 735--760 (2021; Zbl 1488.65412) Full Text: DOI
Deng, Beichuan; Shen, Jie; Zhuang, Qingqu Second-order SAV schemes for the nonlinear Schrödinger equation and their error analysis. (English) Zbl 1491.65111 J. Sci. Comput. 88, No. 3, Paper No. 69, 24 p. (2021). MSC: 65M70 65M06 65N35 65L06 65D30 65M12 65M15 35Q55 35Q41 PDFBibTeX XMLCite \textit{B. Deng} et al., J. Sci. Comput. 88, No. 3, Paper No. 69, 24 p. (2021; Zbl 1491.65111) Full Text: DOI
Feng, Xiaobing; Li, Buyang; Ma, Shu High-order mass- and energy-conserving SAV-Gauss collocation finite element methods for the nonlinear Schrödinger equation. (English) Zbl 1477.65254 SIAM J. Numer. Anal. 59, No. 3, 1566-1591 (2021). MSC: 65N35 65N30 65N12 65N15 65N50 35C08 35A01 35A02 35Q55 PDFBibTeX XMLCite \textit{X. Feng} et al., SIAM J. Numer. Anal. 59, No. 3, 1566--1591 (2021; Zbl 1477.65254) Full Text: DOI arXiv
Yang, Yun-Bo; Jiang, Yao-Lin; Yu, Bo-Hao Unconditional optimal error estimates of linearized, decoupled and conservative Galerkin FEMs for the Klein-Gordon-Schrödinger equation. (English) Zbl 1476.65259 J. Sci. Comput. 87, No. 3, Paper No. 89, 32 p. (2021). MSC: 65M60 65M06 65N30 65M15 65N15 65N12 35Q55 35Q41 PDFBibTeX XMLCite \textit{Y.-B. Yang} et al., J. Sci. Comput. 87, No. 3, Paper No. 89, 32 p. (2021; Zbl 1476.65259) Full Text: DOI
Guan, Zhen; Wang, Jungang; Nie, Yufeng Unconditionally optimal error estimates of two linearized Galerkin FEMs for the two-dimensional nonlinear fractional Rayleigh-Stokes problem. (English) Zbl 1524.65537 Comput. Math. Appl. 93, 78-93 (2021). MSC: 65M60 65M12 35R11 26A33 65M15 76A05 35Q35 65N30 PDFBibTeX XMLCite \textit{Z. Guan} et al., Comput. Math. Appl. 93, 78--93 (2021; Zbl 1524.65537) Full Text: DOI
Yao, C. H.; Wang, Z. Y.; Zhao, Y. M. A leap-frog finite element method for wave propagation of Maxwell-Schrödinger equations with nonlocal effect in metamaterials. (English) Zbl 1524.65622 Comput. Math. Appl. 90, 25-37 (2021). MSC: 65M60 35Q55 78M10 35Q61 65M15 65M12 65M06 65N30 78M20 78A60 81V80 PDFBibTeX XMLCite \textit{C. H. Yao} et al., Comput. Math. Appl. 90, 25--37 (2021; Zbl 1524.65622) Full Text: DOI
Yang, Yun-Bo; Jiang, Yao-Lin Unconditional optimal error estimates of linearized backward Euler Galerkin FEMs for nonlinear Schrödinger-Helmholtz equations. (English) Zbl 1475.65135 Numer. Algorithms 86, No. 4, 1495-1522 (2021). Reviewer: Vit Dolejsi (Praha) MSC: 65M60 65M06 65N30 65N15 65N12 35Q55 35Q60 PDFBibTeX XMLCite \textit{Y.-B. Yang} and \textit{Y.-L. Jiang}, Numer. Algorithms 86, No. 4, 1495--1522 (2021; Zbl 1475.65135) Full Text: DOI
Henning, Patrick; Wärnegård, Johan A note on optimal \(H^1\)-error estimates for Crank-Nicolson approximations to the nonlinear Schrödinger equation. (English) Zbl 1460.35326 BIT 61, No. 1, 37-59 (2021). MSC: 35Q55 65M60 65M06 65M15 65M12 65N30 65H10 35B45 81Q05 PDFBibTeX XMLCite \textit{P. Henning} and \textit{J. Wärnegård}, BIT 61, No. 1, 37--59 (2021; Zbl 1460.35326) Full Text: DOI arXiv
Li, Zhenzhen; Li, Minghao; Shi, Dongyang Unconditional convergence and superconvergence analysis for the transient Stokes equations with damping. (English) Zbl 1508.76071 Appl. Math. Comput. 389, Article ID 125572, 12 p. (2021). MSC: 76M10 65M60 65M12 65M15 76D07 PDFBibTeX XMLCite \textit{Z. Li} et al., Appl. Math. Comput. 389, Article ID 125572, 12 p. (2021; Zbl 1508.76071) Full Text: DOI
Shi, Dongyang; Liu, Qian Nonconforming quadrilateral \(EQ_1^{rot}\) finite element method for Ginzburg-Landau equation. (English) Zbl 07771393 Numer. Methods Partial Differ. Equations 36, No. 2, 329-341 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{D. Shi} and \textit{Q. Liu}, Numer. Methods Partial Differ. Equations 36, No. 2, 329--341 (2020; Zbl 07771393) Full Text: DOI
Ren, Jincheng; Shi, Dongyang; Vong, Seakweng High accuracy error estimates of a Galerkin finite element method for nonlinear time fractional diffusion equation. (English) Zbl 07771391 Numer. Methods Partial Differ. Equations 36, No. 2, 284-301 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{J. Ren} et al., Numer. Methods Partial Differ. Equations 36, No. 2, 284--301 (2020; Zbl 07771391) Full Text: DOI
Shi, Y. H.; Zhao, Y. M.; Wang, F. L.; Tang, Y. F. Superconvergence analysis of FEM for 2D multi-term time fractional diffusion-wave equations with variable coefficient. (English) Zbl 1480.65345 Int. J. Comput. Math. 97, No. 8, 1621-1635 (2020). MSC: 65N30 35R11 65N12 PDFBibTeX XMLCite \textit{Y. H. Shi} et al., Int. J. Comput. Math. 97, No. 8, 1621--1635 (2020; Zbl 1480.65345) Full Text: DOI
Wang, Tingchun; Wang, Jialing; Guo, Boling Two completely explicit and unconditionally convergent Fourier pseudo-spectral methods for solving the nonlinear Schrödinger equation. (English) Zbl 1453.65366 J. Comput. Phys. 404, Article ID 109116, 21 p. (2020). MSC: 65M70 65M12 65M15 35Q55 PDFBibTeX XMLCite \textit{T. Wang} et al., J. Comput. Phys. 404, Article ID 109116, 21 p. (2020; Zbl 1453.65366) Full Text: DOI
Li, Meng; Shi, Dongyang; Wang, Junjun Unconditional superconvergence analysis of a linearized Crank-Nicolson Galerkin FEM for generalized Ginzburg-Landau equation. (English) Zbl 1437.65197 Comput. Math. Appl. 79, No. 8, 2411-2425 (2020). MSC: 65N30 65M06 65M12 65M15 35Q56 PDFBibTeX XMLCite \textit{M. Li} et al., Comput. Math. Appl. 79, No. 8, 2411--2425 (2020; Zbl 1437.65197) Full Text: DOI arXiv
Zhang, Houchao; Shi, Dongyang; Li, Qingfu Nonconforming finite element method for a generalized nonlinear Schrödinger equation. (English) Zbl 1474.65375 Appl. Math. Comput. 377, Article ID 125141, 20 p. (2020). MSC: 65M60 65M06 65N30 65M15 65M12 35Q55 PDFBibTeX XMLCite \textit{H. Zhang} et al., Appl. Math. Comput. 377, Article ID 125141, 20 p. (2020; Zbl 1474.65375) Full Text: DOI
Cai, Wentao; Wang, Jilu; Wang, Kai Convergence analysis of Crank-Nicolson Galerkin-Galerkin FEMs for miscible displacement in porous media. (English) Zbl 1434.76063 J. Sci. Comput. 83, No. 2, Paper No. 25, 26 p. (2020). MSC: 76M10 76S05 65N30 35Q35 PDFBibTeX XMLCite \textit{W. Cai} et al., J. Sci. Comput. 83, No. 2, Paper No. 25, 26 p. (2020; Zbl 1434.76063) Full Text: DOI
Li, Meng; Huang, Chengming; Ming, Wanyuan A relaxation-type Galerkin FEM for nonlinear fractional Schrödinger equations. (English) Zbl 1434.65186 Numer. Algorithms 83, No. 1, 99-124 (2020). MSC: 65M60 65M06 35R11 65M12 47H40 35Q41 PDFBibTeX XMLCite \textit{M. Li} et al., Numer. Algorithms 83, No. 1, 99--124 (2020; Zbl 1434.65186) Full Text: DOI
Yao, Changhui; Jia, Shanghui A second order numerical scheme for nonlinear Maxwell’s equations using conforming finite element. (English) Zbl 1433.78024 Appl. Math. Comput. 371, Article ID 124940, 12 p. (2020). MSC: 78M10 65M60 65M12 65M15 35Q60 PDFBibTeX XMLCite \textit{C. Yao} and \textit{S. Jia}, Appl. Math. Comput. 371, Article ID 124940, 12 p. (2020; Zbl 1433.78024) Full Text: DOI
Shi, Dongyang; Liu, Qian Unconditional superconvergent analysis of a linearized finite element method for Ginzburg-Landau equation. (English) Zbl 1427.35262 Appl. Numer. Math. 147, 118-128 (2020). MSC: 35Q56 65M06 65M12 65M15 65N15 PDFBibTeX XMLCite \textit{D. Shi} and \textit{Q. Liu}, Appl. Numer. Math. 147, 118--128 (2020; Zbl 1427.35262) Full Text: DOI
Wang, Junjun; Guo, Lijuan A new approach to convergence analysis of linearized finite element method for nonlinear hyperbolic equation. (English) Zbl 1524.65605 Bound. Value Probl. 2019, Paper No. 48, 28 p. (2019). MSC: 65M60 65M12 35L72 35K51 PDFBibTeX XMLCite \textit{J. Wang} and \textit{L. Guo}, Bound. Value Probl. 2019, Paper No. 48, 28 p. (2019; Zbl 1524.65605) Full Text: DOI
Shi, Dongyang; Yang, Huaijun Superconvergence analysis of a new linearized MFEM for nonlinear Schrödinger equation. (English) Zbl 1499.65525 Int. J. Comput. Math. 96, No. 7, 1514-1531 (2019). MSC: 65M60 65M06 65N30 65M12 35Q55 35Q41 PDFBibTeX XMLCite \textit{D. Shi} and \textit{H. Yang}, Int. J. Comput. Math. 96, No. 7, 1514--1531 (2019; Zbl 1499.65525) Full Text: DOI
Feng, Xiaobing; Liu, Hailiang; Ma, Shu Mass- and energy-conserved numerical schemes for nonlinear Schrödinger equations. (English) Zbl 1473.65102 Commun. Comput. Phys. 26, No. 5, 1365-1396 (2019). MSC: 65M06 35Q55 65M12 PDFBibTeX XMLCite \textit{X. Feng} et al., Commun. Comput. Phys. 26, No. 5, 1365--1396 (2019; Zbl 1473.65102) Full Text: DOI arXiv
Shi, Dongyang; Yang, Huaijun Unconditionally optimal error estimates of a new mixed FEM for nonlinear Schrödinger equations. (English) Zbl 1435.65164 Adv. Comput. Math. 45, No. 5-6, 3173-3194 (2019). MSC: 65M60 65M06 65N30 65N15 35Q55 35Q41 PDFBibTeX XMLCite \textit{D. Shi} and \textit{H. Yang}, Adv. Comput. Math. 45, No. 5--6, 3173--3194 (2019; Zbl 1435.65164) Full Text: DOI
Zhang, Zongbiao; Li, Meng; Wang, Zhongchi A linearized Crank-Nicolson Galerkin FEMs for the nonlinear fractional Ginzburg-Landau equation. (English) Zbl 1432.65151 Appl. Anal. 98, No. 15, 2648-2667 (2019). MSC: 65M60 65M06 35R11 35Q56 65M12 65M15 PDFBibTeX XMLCite \textit{Z. Zhang} et al., Appl. Anal. 98, No. 15, 2648--2667 (2019; Zbl 1432.65151) Full Text: DOI
Li, Meng; Shi, Dongyang; Wang, Junjun; Ming, Wanyuan Unconditional superconvergence analysis of the conservative linearized Galerkin FEMs for nonlinear Klein-Gordon-Schrödinger equation. (English) Zbl 1477.65160 Appl. Numer. Math. 142, 47-63 (2019). MSC: 65M60 35Q55 65M12 65M15 PDFBibTeX XMLCite \textit{M. Li} et al., Appl. Numer. Math. 142, 47--63 (2019; Zbl 1477.65160) Full Text: DOI
Wang, Pengfei; Huang, Pengzhan Convergence of the Crank-Nicolson extrapolation scheme for the Korteweg-de Vries equation. (English) Zbl 1419.65074 Appl. Numer. Math. 143, 88-96 (2019). MSC: 65M60 65M06 65L06 35Q53 65M12 65M15 PDFBibTeX XMLCite \textit{P. Wang} and \textit{P. Huang}, Appl. Numer. Math. 143, 88--96 (2019; Zbl 1419.65074) Full Text: DOI
Shi, Dongyang; Liu, Qian Unconditional superconvergent analysis of a new mixed finite element method for Ginzburg-Landau equation. (English) Zbl 1419.65042 Numer. Methods Partial Differ. Equations 35, No. 1, 422-439 (2019). MSC: 65M12 65M60 35Q56 65M15 PDFBibTeX XMLCite \textit{D. Shi} and \textit{Q. Liu}, Numer. Methods Partial Differ. Equations 35, No. 1, 422--439 (2019; Zbl 1419.65042) Full Text: DOI
Cai, Wentao; He, Dongdong; Pan, Kejia A linearized energy-conservative finite element method for the nonlinear Schrödinger equation with wave operator. (English) Zbl 1432.65144 Appl. Numer. Math. 140, 183-198 (2019). MSC: 65M60 65M12 65M15 35Q55 PDFBibTeX XMLCite \textit{W. Cai} et al., Appl. Numer. Math. 140, 183--198 (2019; Zbl 1432.65144) Full Text: DOI arXiv
Xu, Chao; Zhou, Jiaquan; Shi, Dongyang; Zhang, Houchao Low order nonconforming finite element method for time-dependent nonlinear Schrödinger equation. (English) Zbl 1499.65540 Bound. Value Probl. 2018, Paper No. 174, 17 p. (2018). MSC: 65M60 65M06 65N30 65N55 65M12 65M15 35Q55 35Q41 PDFBibTeX XMLCite \textit{C. Xu} et al., Bound. Value Probl. 2018, Paper No. 174, 17 p. (2018; Zbl 1499.65540) Full Text: DOI
Zhang, Houchao; Wang, An A new approach of superconvergence analysis of a low order nonconforming MFEM for reaction-diffusion equation. (English) Zbl 1499.65546 Bound. Value Probl. 2018, Paper No. 169, 20 p. (2018). MSC: 65M60 35K57 65M15 65M12 65N30 65M06 35K91 PDFBibTeX XMLCite \textit{H. Zhang} and \textit{A. Wang}, Bound. Value Probl. 2018, Paper No. 169, 20 p. (2018; Zbl 1499.65546) Full Text: DOI
Zouraris, Georgios E. A linear implicit finite difference discretization of the Schrödinger-Hirota equation. (English) Zbl 1407.65164 J. Sci. Comput. 77, No. 1, 634-656 (2018). MSC: 65M06 65M12 65M15 35C08 35Q55 PDFBibTeX XMLCite \textit{G. E. Zouraris}, J. Sci. Comput. 77, No. 1, 634--656 (2018; Zbl 1407.65164) Full Text: DOI arXiv
Xiong, Chunguang; Luo, Fusheng; Ma, Xiuling Uniform in time error analysis of HDG approximation for Schrödinger equation based on HDG projection. (English) Zbl 1416.65365 ESAIM, Math. Model. Numer. Anal. 52, No. 2, 751-772 (2018). MSC: 65M60 65M15 81Q05 PDFBibTeX XMLCite \textit{C. Xiong} et al., ESAIM, Math. Model. Numer. Anal. 52, No. 2, 751--772 (2018; Zbl 1416.65365) Full Text: DOI
Li, Dongfang; Zhang, Jiwei; Zhang, Zhimin Unconditionally optimal error estimates of a linearized Galerkin method for nonlinear time fractional reaction-subdiffusion equations. (English) Zbl 1397.65173 J. Sci. Comput. 76, No. 2, 848-866 (2018). MSC: 65M30 35R11 35K57 65M06 65M12 35K55 65M15 PDFBibTeX XMLCite \textit{D. Li} et al., J. Sci. Comput. 76, No. 2, 848--866 (2018; Zbl 1397.65173) Full Text: DOI
Li, Meng; Huang, Chengming; Zhang, Zongbiao Unconditional error analysis of Galerkin FEMs for nonlinear fractional Schrödinger equation. (English) Zbl 1448.65167 Appl. Anal. 97, No. 2, 295-315 (2018). MSC: 65M60 65N30 65M06 65M15 35R11 26A33 35Q55 PDFBibTeX XMLCite \textit{M. Li} et al., Appl. Anal. 97, No. 2, 295--315 (2018; Zbl 1448.65167) Full Text: DOI
Shi, Dongyang; Wang, Junjun; Yan, Fengna Unconditional superconvergence analysis of an \(H^1\)-Galerkin mixed finite element method for nonlinear Sobolev equations. (English) Zbl 1390.65120 Numer. Methods Partial Differ. Equations 34, No. 1, 145-166 (2018). Reviewer: T. C. Mohan (Chennai) MSC: 65M60 65M12 PDFBibTeX XMLCite \textit{D. Shi} et al., Numer. Methods Partial Differ. Equations 34, No. 1, 145--166 (2018; Zbl 1390.65120) Full Text: DOI
Cai, Wentao; Li, Jian; Chen, Zhangxin Unconditional optimal error estimates for BDF2-FEM for a nonlinear Schrödinger equation. (English) Zbl 1377.65117 J. Comput. Appl. Math. 331, 23-41 (2018). MSC: 65M15 65M60 35Q55 PDFBibTeX XMLCite \textit{W. Cai} et al., J. Comput. Appl. Math. 331, 23--41 (2018; Zbl 1377.65117) Full Text: DOI
Shi, Dongyang; Yang, Huaijun Unconditional optimal error estimates of a two-grid method for semilinear parabolic equation. (English) Zbl 1427.65184 Appl. Math. Comput. 310, 40-47 (2017). MSC: 65M06 35K20 35K91 65M15 PDFBibTeX XMLCite \textit{D. Shi} and \textit{H. Yang}, Appl. Math. Comput. 310, 40--47 (2017; Zbl 1427.65184) Full Text: DOI
Shi, Dongyang; Wang, Junjun Unconditional superconvergence analysis for nonlinear hyperbolic equation with nonconforming finite element. (English) Zbl 1411.65134 Appl. Math. Comput. 305, 1-16 (2017). MSC: 65M60 65M12 PDFBibTeX XMLCite \textit{D. Shi} and \textit{J. Wang}, Appl. Math. Comput. 305, 1--16 (2017; Zbl 1411.65134) Full Text: DOI
Shi, Dongyang; Wang, Junjun Unconditional superconvergence analysis of conforming finite element for nonlinear parabolic equation. (English) Zbl 1411.65133 Appl. Math. Comput. 294, 216-226 (2017). MSC: 65M60 35K20 35K59 65M12 PDFBibTeX XMLCite \textit{D. Shi} and \textit{J. Wang}, Appl. Math. Comput. 294, 216--226 (2017; Zbl 1411.65133) Full Text: DOI
Shi, Dongyang; Wang, Junjun Unconditional superconvergence analysis of a linearized Galerkin FEM for nonlinear hyperbolic equations. (English) Zbl 1384.65062 Comput. Math. Appl. 74, No. 4, 634-651 (2017). MSC: 65M12 65M60 35L70 65M15 PDFBibTeX XMLCite \textit{D. Shi} and \textit{J. Wang}, Comput. Math. Appl. 74, No. 4, 634--651 (2017; Zbl 1384.65062) Full Text: DOI
Li, Dongfang; Wang, Jilu; Zhang, Jiwei Unconditionally convergent \(L1\)-Galerkin FEMs for nonlinear time-fractional Schrödinger equations. (English) Zbl 1379.65079 SIAM J. Sci. Comput. 39, No. 6, A3067-A3088 (2017). MSC: 65M60 35Q55 35R11 65M15 65M12 PDFBibTeX XMLCite \textit{D. Li} et al., SIAM J. Sci. Comput. 39, No. 6, A3067--A3088 (2017; Zbl 1379.65079) Full Text: DOI
Li, Dongfang; Wang, Jilu Unconditionally optimal error analysis of Crank-Nicolson Galerkin FEMs for a strongly nonlinear parabolic system. (English) Zbl 1377.65118 J. Sci. Comput. 72, No. 2, 892-915 (2017). Reviewer: Marius Ghergu (Dublin) MSC: 65M15 65M60 35K55 65M06 PDFBibTeX XMLCite \textit{D. Li} and \textit{J. Wang}, J. Sci. Comput. 72, No. 2, 892--915 (2017; Zbl 1377.65118) Full Text: DOI
Shi, Dongyang; Wang, Junjun Unconditional superconvergence analysis of a Crank-Nicolson Galerkin FEM for nonlinear Schrödinger equation. (English) Zbl 1407.65162 J. Sci. Comput. 72, No. 3, 1093-1118 (2017). Reviewer: Elena V. Tabarintseva (Chelyabinsk) MSC: 65M12 65M06 65M60 35Q55 PDFBibTeX XMLCite \textit{D. Shi} and \textit{J. Wang}, J. Sci. Comput. 72, No. 3, 1093--1118 (2017; Zbl 1407.65162) Full Text: DOI
Henning, Patrick; Peterseim, Daniel Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials. (English) Zbl 1377.65128 Math. Models Methods Appl. Sci. 27, No. 11, 2147-2184 (2017). Reviewer: T. C. Mohan (Chennai) MSC: 65M60 35Q55 65M06 65M12 PDFBibTeX XMLCite \textit{P. Henning} and \textit{D. Peterseim}, Math. Models Methods Appl. Sci. 27, No. 11, 2147--2184 (2017; Zbl 1377.65128) Full Text: DOI arXiv
Henning, Patrick; Målqvist, Axel The finite element method for the time-dependent Gross-Pitaevskii equation with angular momentum rotation. (English) Zbl 1362.65105 SIAM J. Numer. Anal. 55, No. 2, 923-952 (2017). MSC: 65M60 65M15 35J10 PDFBibTeX XMLCite \textit{P. Henning} and \textit{A. Målqvist}, SIAM J. Numer. Anal. 55, No. 2, 923--952 (2017; Zbl 1362.65105) Full Text: DOI arXiv
Shi, Dongyang; Wang, Junjun; Yan, Fengna Unconditional superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{rot}\) nonconforming finite element. (English) Zbl 1368.65162 J. Sci. Comput. 70, No. 1, 85-111 (2017). Reviewer: Charis Harley (Johannesburg) MSC: 65M12 65M60 35K55 65M15 PDFBibTeX XMLCite \textit{D. Shi} et al., J. Sci. Comput. 70, No. 1, 85--111 (2017; Zbl 1368.65162) Full Text: DOI
Wang, Jianyun; Huang, Yunqing; Tian, Zhikun; Zhou, Jie Superconvergence analysis of finite element method for the time-dependent Schrödinger equation. (English) Zbl 1443.65225 Comput. Math. Appl. 71, No. 10, 1960-1972 (2016). MSC: 65M60 65M12 35Q55 PDFBibTeX XMLCite \textit{J. Wang} et al., Comput. Math. Appl. 71, No. 10, 1960--1972 (2016; Zbl 1443.65225) Full Text: DOI
Shi, Dongyang; Liao, Xin; Wang, Lele Superconvergence analysis of conforming finite element method for nonlinear Schrödinger equation. (English) Zbl 1410.65378 Appl. Math. Comput. 289, 298-310 (2016). MSC: 65M60 35Q55 65M12 PDFBibTeX XMLCite \textit{D. Shi} et al., Appl. Math. Comput. 289, 298--310 (2016; Zbl 1410.65378) Full Text: DOI