Ren, Haoran; Liu, Yang; Yin, Baoli; Li, Hong Finite element algorithm with a second-order shifted composite numerical integral formula for a nonlinear time fractional wave equation. (English) Zbl 07798418 Numer. Methods Partial Differ. Equations 40, No. 1, Article ID e23066, 23 p. (2024). MSC: 65L10 65R20 35L05 PDFBibTeX XMLCite \textit{H. Ren} et al., Numer. Methods Partial Differ. Equations 40, No. 1, Article ID e23066, 23 p. (2024; Zbl 07798418) 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, Junjun Superconvergence analysis of an energy stable scheme with three step backward differential formula-finite element method for nonlinear reaction-diffusion equation. (English) Zbl 07779698 Numer. Methods Partial Differ. Equations 39, No. 1, 30-44 (2023). MSC: 65M60 65M06 65N30 65M12 65M15 65N15 PDFBibTeX XMLCite \textit{J. Wang}, Numer. Methods Partial Differ. Equations 39, No. 1, 30--44 (2023; Zbl 07779698) Full Text: DOI
Adak, Dibyendu Convergence analysis of expanded mixed virtual element methods for nonlocal problems. (English) Zbl 07777354 Numer. Methods Partial Differ. Equations 39, No. 4, 3246-3270 (2023). MSC: 65M60 65M06 65N30 65M15 35R09 45K05 47H10 PDFBibTeX XMLCite \textit{D. Adak}, Numer. Methods Partial Differ. Equations 39, No. 4, 3246--3270 (2023; Zbl 07777354) 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
Lin, Xiuxiu; Chen, Yanping; Huang, Yunqing Spectral approximation for optimal control problems governed by first bi-harmonic equation. (English) Zbl 07777335 Numer. Methods Partial Differ. Equations 39, No. 4, 2808-2822 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{X. Lin} et al., Numer. Methods Partial Differ. Equations 39, No. 4, 2808--2822 (2023; Zbl 07777335) Full Text: DOI
Yang, Jiming; Zhou, Jing; Su, Yifan A two-grid discontinuous Galerkin method for an incompressible miscible displacement problem. (English) Zbl 07777333 Numer. Methods Partial Differ. Equations 39, No. 4, 2763-2786 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{J. Yang} et al., Numer. Methods Partial Differ. Equations 39, No. 4, 2763--2786 (2023; Zbl 07777333) Full Text: DOI
Sayevand, Khosro; Mirzaee, Farshid; Masti, Imman On two-dimensional weakly singular fractional partial integro-differential equations and dual Bernstein polynomials. (English) Zbl 07777017 Numer. Methods Partial Differ. Equations 39, No. 3, 2538-2560 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{K. Sayevand} et al., Numer. Methods Partial Differ. Equations 39, No. 3, 2538--2560 (2023; Zbl 07777017) Full Text: DOI
Zheng, Weishan; Chen, Yanping A spectral collocation method for a nonlinear multidimensional Volterra integral equation. (English) Zbl 07776982 Numer. Methods Partial Differ. Equations 39, No. 2, 1767-1777 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{W. Zheng} and \textit{Y. Chen}, Numer. Methods Partial Differ. Equations 39, No. 2, 1767--1777 (2023; Zbl 07776982) Full Text: DOI
Gupta, Aastha; Kaushik, Aditya; Sharma, Manju A higher-order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction-diffusion problems with Robin-boundary conditions. (English) Zbl 07776960 Numer. Methods Partial Differ. Equations 39, No. 2, 1220-1250 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{A. Gupta} et al., Numer. Methods Partial Differ. Equations 39, No. 2, 1220--1250 (2023; Zbl 07776960) Full Text: DOI
Zhang, Jiaqi; Yang, Yin An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint. (English) Zbl 07769122 Numer. Methods Partial Differ. Equations 39, No. 6, 4403-4420 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{J. Zhang} and \textit{Y. Yang}, Numer. Methods Partial Differ. Equations 39, No. 6, 4403--4420 (2023; Zbl 07769122) Full Text: DOI
Chu, Xiaochen; Chen, Chuanjun; Zhang, Tong Two-level stabilized finite volume method for the stationary incompressible magnetohydrodynamic equations. (English) Zbl 07769114 Numer. Methods Partial Differ. Equations 39, No. 6, 4196-4220 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{X. Chu} et al., Numer. Methods Partial Differ. Equations 39, No. 6, 4196--4220 (2023; Zbl 07769114) Full Text: DOI
Wang, Fangyuan; Zhou, Zhaojie Spectral Galerkin method for state constrained optimal control of fractional advection-diffusion-reaction equations. (English) Zbl 07778306 Numer. Methods Partial Differ. Equations 38, No. 5, 1526-1542 (2022). MSC: 65N35 65N30 49M41 35B45 33C45 26A33 35R11 PDFBibTeX XMLCite \textit{F. Wang} and \textit{Z. Zhou}, Numer. Methods Partial Differ. Equations 38, No. 5, 1526--1542 (2022; Zbl 07778306) Full Text: DOI
Darehmiraki, Majid; Rezazadeh, Arezou; Ahmadian, Ali; Salahshour, Soheil An interpolation method for the optimal control problem governed by the elliptic convection-diffusion equation. (English) Zbl 07777078 Numer. Methods Partial Differ. Equations 38, No. 2, 137-159 (2022). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{M. Darehmiraki} et al., Numer. Methods Partial Differ. Equations 38, No. 2, 137--159 (2022; Zbl 07777078) Full Text: DOI
Zhang, Yuanyuan; Liu, Xiaoping A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems. (English) Zbl 07775894 Numer. Methods Partial Differ. Equations 38, No. 1, 48-64 (2022). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{Y. Zhang} and \textit{X. Liu}, Numer. Methods Partial Differ. Equations 38, No. 1, 48--64 (2022; Zbl 07775894) Full Text: DOI
Yang, Huaijun; Shi, Dongyang; Zhang, Li-Tao Unconditionally optimal error estimates of BDF2 Galerkin method for semilinear parabolic equation. (English) Zbl 07776083 Numer. Methods Partial Differ. Equations 37, No. 3, 2511-2526 (2021). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{H. Yang} et al., Numer. Methods Partial Differ. Equations 37, No. 3, 2511--2526 (2021; Zbl 07776083) Full Text: DOI
Kumar, Sunil; Ghosh, Surath; Kumar, Ranbir; Jleli, Mohamed A fractional model for population dynamics of two interacting species by using spectral and Hermite wavelets methods. (English) Zbl 07776037 Numer. Methods Partial Differ. Equations 37, No. 2, 1652-1672 (2021). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{S. Kumar} et al., Numer. Methods Partial Differ. Equations 37, No. 2, 1652--1672 (2021; Zbl 07776037) Full Text: DOI
Li, Qing; Yang, Qing; Chen, Huanzhen Compact difference scheme for two-dimensional fourth-order nonlinear hyperbolic equation. (English) Zbl 07777680 Numer. Methods Partial Differ. Equations 36, No. 6, 1938-1961 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{Q. Li} et al., Numer. Methods Partial Differ. Equations 36, No. 6, 1938--1961 (2020; Zbl 07777680) Full Text: DOI
Liu, Yang; Liu, Nan; Li, Hong; Wang, Jinfeng Fast calculation based on a spatial two-grid finite element algorithm for a nonlinear space-time fractional diffusion model. (English) Zbl 07777678 Numer. Methods Partial Differ. Equations 36, No. 6, 1904-1921 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{Y. Liu} et al., Numer. Methods Partial Differ. Equations 36, No. 6, 1904--1921 (2020; Zbl 07777678) Full Text: DOI
Zhang, Jiansong; Han, Huiran; Guo, Hui; Shen, Xiaomang A combined hybrid mixed element method for incompressible miscible displacement problem with local discontinuous Galerkin procedure. (English) Zbl 07777664 Numer. Methods Partial Differ. Equations 36, No. 6, 1629-1647 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{J. Zhang} et al., Numer. Methods Partial Differ. Equations 36, No. 6, 1629--1647 (2020; Zbl 07777664) Full Text: DOI
Guan, Hongbo; Shi, Dongyang Superconvergence analysis of a nonconforming finite element method for monotone semilinear elliptic optimal control problems. (English) Zbl 07777654 Numer. Methods Partial Differ. Equations 36, No. 6, 1405-1417 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{H. Guan} and \textit{D. Shi}, Numer. Methods Partial Differ. Equations 36, No. 6, 1405--1417 (2020; Zbl 07777654) Full Text: DOI
Hou, Tianliang; Leng, Haitao; Luan, Tian Two-grid methods for \(P_0^2\)-\(P_1\) mixed finite element approximation of general elliptic optimal control problems with low regularity. (English) Zbl 07771433 Numer. Methods Partial Differ. Equations 36, No. 5, 1184-1202 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{T. Hou} et al., Numer. Methods Partial Differ. Equations 36, No. 5, 1184--1202 (2020; Zbl 07771433) Full Text: DOI
Lyu, Pin; Vong, Seakweng A nonuniform L2 formula of Caputo derivative and its application to a fractional Benjamin-Bona-Mahony-type equation with nonsmooth solutions. (English) Zbl 07771404 Numer. Methods Partial Differ. Equations 36, No. 3, 579-600 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{P. Lyu} and \textit{S. Vong}, Numer. Methods Partial Differ. Equations 36, No. 3, 579--600 (2020; Zbl 07771404) Full Text: DOI
Al-Taweel, Ahmed; Hussain, Saqib; Wang, Xiaoshen; Jones, Brian A \(P_0\)-\(P_0\) weak Galerkin finite element method for solving singularly perturbed reaction-diffusion problems. (English) Zbl 07771387 Numer. Methods Partial Differ. Equations 36, No. 2, 213-227 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{A. Al-Taweel} et al., Numer. Methods Partial Differ. Equations 36, No. 2, 213--227 (2020; Zbl 07771387) Full Text: DOI
Shi, Dongyang; Yang, Huaijun Superconvergent estimates of conforming finite element method for nonlinear time-dependent joule heating equations. (English) Zbl 1390.65056 Numer. Methods Partial Differ. Equations 34, No. 1, 336-356 (2018). Reviewer: Ivan Secrieru (Chişinău) MSC: 65M60 65M12 65M15 78M10 PDFBibTeX XMLCite \textit{D. Shi} and \textit{H. Yang}, Numer. Methods Partial Differ. Equations 34, No. 1, 336--356 (2018; Zbl 1390.65056) Full Text: DOI
Qiu, Hailong; Mei, Liquan; Zhang, Yongchao Two-grid variational multiscale algorithms for the stationary incompressible Navier-Stokes equations with friction boundary conditions. (English) Zbl 1457.76058 Numer. Methods Partial Differ. Equations 33, No. 2, 546-569 (2017). MSC: 76D05 76M30 65M15 PDFBibTeX XMLCite \textit{H. Qiu} et al., Numer. Methods Partial Differ. Equations 33, No. 2, 546--569 (2017; Zbl 1457.76058) Full Text: DOI
Luo, Xianbing A priori error estimates of Crank-Nicolson finite volume element method for a hyperbolic optimal control problem. (English) Zbl 1405.65106 Numer. Methods Partial Differ. Equations 32, No. 5, 1331-1356 (2016). MSC: 65M08 49M25 65M15 PDFBibTeX XMLCite \textit{X. Luo}, Numer. Methods Partial Differ. Equations 32, No. 5, 1331--1356 (2016; Zbl 1405.65106) Full Text: DOI
Wang, Zhu Nonlinear model reduction based on the finite element method with interpolated coefficients: Semilinear parabolic equations. (English) Zbl 1334.65159 Numer. Methods Partial Differ. Equations 31, No. 6, 1713-1741 (2015). MSC: 65M60 35K58 65M15 PDFBibTeX XMLCite \textit{Z. Wang}, Numer. Methods Partial Differ. Equations 31, No. 6, 1713--1741 (2015; Zbl 1334.65159) Full Text: DOI arXiv
Münzenmaier, Steffen First-order system least squares for generalized-Newtonian coupled Stokes-Darcy flow. (English) Zbl 1329.76183 Numer. Methods Partial Differ. Equations 31, No. 4, 1150-1173 (2015). MSC: 76M10 65N30 65N50 76S05 PDFBibTeX XMLCite \textit{S. Münzenmaier}, Numer. Methods Partial Differ. Equations 31, No. 4, 1150--1173 (2015; Zbl 1329.76183) Full Text: DOI
He, Wen-Ming; Cui, Jun-Zhi; Zhu, Qi-Ding; Wen, Zhong-Liang The local superconvergence of the linear finite element method for the Poisson problem. (English) Zbl 1297.65133 Numer. Methods Partial Differ. Equations 30, No. 3, 930-946 (2014). Reviewer: Ariadna Lucia Pletea (Iaşi) MSC: 65N12 65N30 35J05 65N80 PDFBibTeX XMLCite \textit{W.-M. He} et al., Numer. Methods Partial Differ. Equations 30, No. 3, 930--946 (2014; Zbl 1297.65133) Full Text: DOI
Guo, Hui; Fu, Hongfei; Zhang, Jiansong Superconvergence of the split least-squares method for second-order hyperbolic equations. (English) Zbl 1283.65083 Numer. Methods Partial Differ. Equations 30, No. 1, 222-238 (2014). Reviewer: H. P. Dikshit (Bhopal) MSC: 65M12 65M60 35L20 PDFBibTeX XMLCite \textit{H. Guo} et al., Numer. Methods Partial Differ. Equations 30, No. 1, 222--238 (2014; Zbl 1283.65083) Full Text: DOI
Yang, Jiming; Chen, Yanping; Xiong, Zhiguang Superconvergence of a full-discrete combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem. (English) Zbl 1277.76049 Numer. Methods Partial Differ. Equations 29, No. 6, 1801-1820 (2013). MSC: 76M10 76S05 PDFBibTeX XMLCite \textit{J. Yang} et al., Numer. Methods Partial Differ. Equations 29, No. 6, 1801--1820 (2013; Zbl 1277.76049) Full Text: DOI
Hou, Tianliang Error estimates of expanded mixed methods for optimal control problems governed by hyperbolic integro-differential equations. (English) Zbl 1274.65179 Numer. Methods Partial Differ. Equations 29, No. 5, 1675-1693 (2013). MSC: 65K10 65R20 45J05 49J99 PDFBibTeX XMLCite \textit{T. Hou}, Numer. Methods Partial Differ. Equations 29, No. 5, 1675--1693 (2013; Zbl 1274.65179) Full Text: DOI
Chen, Chuanjun; Liu, Wei; Bi, Chunjia A two-grid characteristic finite volume element method for semilinear advection-dominated diffusion equations. (English) Zbl 1274.65252 Numer. Methods Partial Differ. Equations 29, No. 5, 1543-1562 (2013). MSC: 65M08 65M25 PDFBibTeX XMLCite \textit{C. Chen} et al., Numer. Methods Partial Differ. Equations 29, No. 5, 1543--1562 (2013; Zbl 1274.65252) Full Text: DOI
Chen, Yanping; Chen, Luoping; Zhang, Xiaochun Two-grid method for nonlinear parabolic equations by expanded mixed finite element methods. (English) Zbl 1322.65094 Numer. Methods Partial Differ. Equations 29, No. 4, 1238-1256 (2013). MSC: 65M60 35K57 65M15 65M55 PDFBibTeX XMLCite \textit{Y. Chen} et al., Numer. Methods Partial Differ. Equations 29, No. 4, 1238--1256 (2013; Zbl 1322.65094) Full Text: DOI
Liu, Yang; Li, Hong; Wang, Jinfeng; He, Siriguleng Splitting positive definite mixed element methods for pseudo-hyperbolic equations. (English) Zbl 1245.65129 Numer. Methods Partial Differ. Equations 28, No. 2, 670-688 (2012). Reviewer: Qin Mengzhao (Beijing) MSC: 65M60 35L82 65M20 65M15 PDFBibTeX XMLCite \textit{Y. Liu} et al., Numer. Methods Partial Differ. Equations 28, No. 2, 670--688 (2012; Zbl 1245.65129) Full Text: DOI
Wang, Cheng Convergence of the interpolated coefficient finite element method for the two-dimensional elliptic sine-Gordon equations. (English) Zbl 1228.65213 Numer. Methods Partial Differ. Equations 27, No. 2, 387-398 (2011). Reviewer: Ariadna Lucia Pletea (Iaşi) MSC: 65N12 65N30 35Q40 35J60 PDFBibTeX XMLCite \textit{C. Wang}, Numer. Methods Partial Differ. Equations 27, No. 2, 387--398 (2011; Zbl 1228.65213) Full Text: DOI
Lazarov, Raytcho; Repin, Sergey; Tomar, Satyendra K. Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems. (English) Zbl 1167.65451 Numer. Methods Partial Differ. Equations 25, No. 4, 952-971 (2009). MSC: 65N15 65N30 PDFBibTeX XMLCite \textit{R. Lazarov} et al., Numer. Methods Partial Differ. Equations 25, No. 4, 952--971 (2009; Zbl 1167.65451) Full Text: DOI