Anisotropic Biquadratic Element with Superclose Result. - Dongyang Shi; Shipeng Mao; Hui Liang (J. Syst. Sci. Complex., 2006)

Superconvergence Analysis of a Nonconforming Triangular Element on Anisotropic Meshes. - Dongyang Shi; Hui Liang; Caixia Wang (J. Syst. Sci. Complex., 2007)

Accuracy Analysis for Quasi-Carey Element. - Dongyang Shi; Xiaobin Hao (J. Syst. Sci. Complex., 2008)

Convergence and superconvergence analysis of a new quadratic Hermite-type triangular element on anisotropic meshes. - Dongyang Shi; Hui Liang (Appl. Math. Comput., 2009)

Low order Crouzeix-Raviart type nonconforming finite element methods for the 3D time-dependent Maxwell's equations. - Dongyang Shi; Lifang Pei (Appl. Math. Comput., 2009)

A new second order nonconforming mixed finite element scheme for the stationary Stokes and Navier-Stokes equations. - Dongyang Shi; Jincheng Ren; Xiaobin Hao (Appl. Math. Comput., 2009)

Error estimates for rotated Q1rot element approximation of the eigenvalue problem on anisotropic meshes. - Dongyang Shi; Yucheng Peng; Shaochun Chen (Appl. Math. Lett., 2009)

A low order nonconforming anisotropic finite element approximation to parabolic problem. - Dongyang Shi; Wei Gong 005 (J. Syst. Sci. Complex., 2009)

Convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument. - Hui Liang 001; Dongyang Shi; Wanjin Lv (Appl. Math. Comput., 2010)

A new robust C0-type nonconforming triangular element for singular perturbation problems. - Pingli Xie; Dongyang Shi; Hua Li (Appl. Math. Comput., 2010)

Nonconforming finite element method for nonlinear parabolic equations. - Dongyang Shi; Buying Zhang (J. Syst. Sci. Complex., 2010)

High accuracy analysis of a new nonconforming mixed finite element scheme for Sobolev equations. - Dongyang Shi; Yadong Zhang (Appl. Math. Comput., 2011)

A new low-order non-conforming mixed finite-element scheme for second-order elliptic problems. - Dongyang Shi; Caixia Wang (Int. J. Comput. Math., 2011)

High accuracy analysis of the finite element method for nonlinear viscoelastic wave equations with nonlinear boundary conditions. - Dongyang Shi; Buying Zhang (J. Syst. Sci. Complex., 2011)

A new stable second order nonconforming mixed finite element scheme for the stationary Stokes and Navier-Stokes equations. - Dongyang Shi; Wei Gong 005; Jincheng Ren (Math. Comput. Model., 2011)

Superconvergence Analysis of Finite Element Method for a Second-Type Variational Inequality. - Dongyang Shi; Hongbo Guan; Xiaofei Guan (J. Appl. Math., 2012)

Low-Order Nonconforming Mixed Finite Element Methods for Stationary Incompressible Magnetohydrodynamics Equations. - Dongyang Shi; Zhiyun Yu (J. Appl. Math., 2012)

Nonconforming quadrilateral finite element method for a class of nonlinear sine-Gordon equations. - Dongyang Shi; Lifang Pei (Appl. Math. Comput., 2013)

Superclose and superconvergence of finite element discretizations for the Stokes equations with damping. - Dongyang Shi; Zhiyun Yu (Appl. Math. Comput., 2013)

A new low order least squares nonconforming characteristics mixed finite element method For Burgers' equation. - Dongyang Shi; Jiaquan Zhou; Dongwei Shi (Appl. Math. Comput., 2013)

Convergence of an iterative method for solving a class of nonlinear equations. - Xiuhua Wang 002; Jisheng Kou; Dongyang Shi (Comput. Math. Appl., 2013)

Superconvergence of an H1-Galerkin nonconforming mixed finite element method for a parabolic equation. - Yadong Zhang; Dongyang Shi (Comput. Math. Appl., 2013)

A New Characteristic Nonconforming Mixed Finite Element Scheme for Convection-Dominated Diffusion Problem. - Dongyang Shi; Qili Tang; Yadong Zhang (J. Appl. Math., 2013)

Anisotropic Nonconforming $${ EQ}_1^{rot}$$ Quadrilateral Finite Element Approximation to Second Order Elliptic Problems. - Dongyang Shi; Chao Xu; Jin-huan Chen (J. Sci. Comput., 2013)

A high accuracy NFEM for constrained optimal control problems governed by elliptic equations. - Hongbo Guan; Dongyang Shi (Appl. Math. Comput., 2014)

Quasi-Wilson nonconforming element approximation for nonlinear dual phase lagging heat conduction equations. - Dongyang Shi; Yanmin Zhao; Fenling Wang (Appl. Math. Comput., 2014)

Superconvergence analysis of anisotropic linear triangular finite element for nonlinear Schrödinger equation. - Dongyang Shi; Pingli Wang; Yanmin Zhao (Appl. Math. Lett., 2014)

The lowest order characteristic mixed finite element scheme for convection-dominated diffusion problem. - Dongyang Shi; Xin Liao; Lele Wang 002 (Comput. Math. Appl., 2014)

Convergence analysis for a family of improved super-Halley methods under general convergence condition. - Xiuhua Wang 002; Dongyang Shi; Jisheng Kou (Numer. Algorithms, 2014)

A stable nonconforming mixed finite element scheme for elliptic optimal control problems. - Hongbo Guan; Dongyang Shi (Comput. Math. Appl., 2015)

Nonconforming finite element analysis for Poisson eigenvalue problem. - Dongyang Shi; Lele Wang 002; Xin Liao (Comput. Math. Appl., 2015)

The Brezzi-Pitkäranta stabilization scheme for the elasticity problem. - Minghao Li; Dongyang Shi; Ying Dai (J. Comput. Appl. Math., 2015)

A New Stabilization Method for the Elasticity Problem. - Dongyang Shi; Minghao Li; Chao Xu (J. Sci. Comput., 2015)

A low order characteristic-nonconforming finite element method for nonlinear Sobolev equation with convection-dominated term. - Dongyang Shi; Qili Tang; Wei Gong 005 (Math. Comput. Simul., 2015)

Superconvergence analysis of conforming finite element method for nonlinear Schrödinger equation. - Dongyang Shi; Xin Liao; Lele Wang 002 (Appl. Math. Comput., 2016)

A new nonconforming mixed finite element scheme for second order eigenvalue problem. - Dongyang Shi; Lele Wang 002; Xin Liao (Appl. Math. Comput., 2016)

Unconditional superconvergence analysis of a new mixed finite element method for nonlinear Sobolev equation. - Dongyang Shi; Fengna Yan; Junjun Wang (Appl. Math. Comput., 2016)

High accuracy analysis of nonconforming MFEM for constrained optimal control problems governed by Stokes equations. - Hongbo Guan; Dongyang Shi; Xiaofei Guan (Appl. Math. Lett., 2016)

A new approach of superconvergence analysis for nonlinear BBM equation on anisotropic meshes. - Dongyang Shi; Huaijun Yang (Appl. Math. Lett., 2016)

Superconvergence analysis of nonconforming finite element method for two-dimensional time fractional diffusion equations. - Yanmin Zhao; Yadong Zhang; Dongyang Shi; Fawang Liu; Ian W. Turner (Appl. Math. Lett., 2016)

Superconvergence analysis of an H1-Galerkin mixed finite element method for Sobolev equations. - Dongyang Shi; Junjun Wang (Comput. Math. Appl., 2016)

Unconditional superconvergence analysis of conforming finite element for nonlinear parabolic equation. - Dongyang Shi; Junjun Wang (Appl. Math. Comput., 2017)

Unconditional superconvergence analysis for nonlinear hyperbolic equation with nonconforming finite element. - Dongyang Shi; Junjun Wang (Appl. Math. Comput., 2017)

Unconditional optimal error estimates of a two-grid method for semilinear parabolic equation. - Dongyang Shi; Huaijun Yang (Appl. Math. Comput., 2017)

A new error analysis of Bergan's energy-orthogonal element for a plate contact problem. - Lifang Pei; Dongyang Shi (Appl. Math. Lett., 2017)

Unconditional superconvergence analysis of a linearized Galerkin FEM for nonlinear hyperbolic equations. - Dongyang Shi; Junjun Wang (Comput. Math. Appl., 2017)

Unconditional Superconvergence Analysis of a Crank-Nicolson Galerkin FEM for Nonlinear Schrödinger Equation. - Dongyang Shi; Junjun Wang (J. Sci. Comput., 2017)

Unconditional Superconvergence Analysis for Nonlinear Parabolic Equation with EQ1rot Nonconforming Finite Element. - Dongyang Shi; Junjun Wang; Fengna Yan (J. Sci. Comput., 2017)

Superconvergence analysis of finite element method for time-fractional Thermistor problem. - Dongyang Shi; Huaijun Yang (Appl. Math. Comput., 2018)

Superconvergence analysis of a two-grid method for semilinear parabolic equations. - Dongyang Shi; Pengcong Mu; Huaijun Yang (Appl. Math. Lett., 2018)

A new approach of superconvergence analysis for two-dimensional time fractional diffusion equation. - Dongyang Shi; Huaijun Yang (Comput. Math. Appl., 2018)

Unconditionally optimal error estimates of a new mixed FEM for nonlinear Schrödinger equations. - Dongyang Shi; Huaijun Yang (Adv. Comput. Math., 2019)

A nonconforming finite element method for the stationary Smagorinsky model. - Dongyang Shi; Minghao Li; Zhenzhen Li (Appl. Math. Comput., 2019)

Superconvergence analysis of nonconforming FEM for nonlinear time-dependent thermistor problem. - Dongyang Shi; Huaijun Yang (Appl. Math. Comput., 2019)

Superconvergence analysis of low order nonconforming finite element methods for variational inequality problem with displacement obstacle. - Chao Xu; Dongyang Shi (Appl. Math. Comput., 2019)

An efficient nonconforming finite element two-grid method for Allen-Cahn equation. - Dongyang Shi; Qian Liu (Appl. Math. Lett., 2019)

Uniform superconvergent analysis of a new mixed finite element method for nonlinear Bi-wave singular perturbation problem. - Dongyang Shi; Yanmi Wu (Appl. Math. Lett., 2019)

An efficient NFEM for optimal control problems governed by a bilinear state equation. - Hongbo Guan; Dongyang Shi (Comput. Math. Appl., 2019)

Superconvergence analysis of a new linearized MFEM for nonlinear Schrödinger equation. - Dongyang Shi; Huaijun Yang (Int. J. Comput. Math., 2019)

Superconvergence analysis of a two grid finite element method for Ginzburg-Landau equation. - Dongyang Shi; Qian Liu (Appl. Math. Comput., 2020)

Uniformly superconvergent analysis of an efficient two-grid method for nonlinear Bi-wave singular perturbation problem. - Dongyang Shi; Yanmi Wu (Appl. Math. Comput., 2020)

Nonconforming finite element method for a generalized nonlinear Schrödinger equation. - Houchao Zhang; Dongyang Shi; Qingfu Li (Appl. Math. Comput., 2020)

Superconvergence analysis of the lowest order rectangular Raviart-Thomas element for semilinear parabolic equation. - Huaijun Yang; Dongyang Shi (Appl. Math. Lett., 2020)

Unconditional superconvergence analysis of a linearized Crank-Nicolson Galerkin FEM for generalized Ginzburg-Landau equation. - Meng Li 025; Dongyang Shi; Junjun Wang (Comput. Math. Appl., 2020)

Superconvergent analysis of a nonconforming mixed finite element method for non-stationary conduction-convection problem. - Dongyang Shi; Qian Liu (Comput. Math. Appl., 2020)

Superconvergence analysis of a two-grid method for nonlinear hyperbolic equations. - Yifan Wei 002; Dongyang Shi (Comput. Math. Appl., 2020)

Superconvergence analysis of a two-grid method for an energy-stable Ciarlet-Raviart type scheme of Cahn-Hilliard equation. - Qian Liu; Dongyang Shi (Numer. Algorithms, 2020)

Unconditional convergence and superconvergence analysis for the transient Stokes equations with damping. - Zhenzhen Li; Minghao Li; Dongyang Shi (Appl. Math. Comput., 2021)

Quasi-uniform and unconditional superconvergence analysis of Ciarlet-Raviart scheme for the fourth order singularly perturbed Bi-wave problem modeling d-wave superconductors. - Yanmi Wu; Dongyang Shi (Appl. Math. Comput., 2021)

Nonconforming Quasi-Wilson finite element approximation for the nonlinear Rosenau equation. - Dongyang Shi; Xu Jia (Appl. Math. Lett., 2021)

Superconvergent analysis of a nonconforming mixed finite element method for time-dependent damped Navier-Stokes equations. - Qian Liu; Dongyang Shi (Comput. Appl. Math., 2021)

Superconvergence analysis of a mixed finite element approximation for the nonlinear fourth-order Rosenau-RLW equation. - Dongyang Shi; Xu Jia (Comput. Math. Appl., 2021)

Multiscale analysis and algorithm of transient electromagnetic scattering from heterogeneous materials. - Yongwei Zhang 003; Liqun Cao; Dongyang Shi; Yanping Lin (J. Comput. Appl. Math., 2021)

Two efficient spectral methods for the nonlinear fractional wave equation in unbounded domain. - Nan Wang; Dongyang Shi (Math. Comput. Simul., 2021)

Superconvergence analysis of two-grid methods for bacteria equations. - Dongyang Shi; Chaoqun Li (Numer. Algorithms, 2021)

Efficient Multiscale Algorithms for Simulating Nonlocal Optical Response of Metallic Nanostructure Arrays. - Yongwei Zhang 003; Chupeng Ma; Li-Qun Cao; Dongyang Shi (SIAM J. Sci. Comput., 2021)

High accuracy analysis of Galerkin finite element method for Klein-Gordon-Zakharov equations. - Dongyang Shi; Ran Wang (Appl. Math. Comput., 2022)

A linearized conservative nonconforming FEM for nonlinear Klein-Gordon-Schrödinger equations. - Dongyang Shi; Houchao Zhang (Comput. Math. Appl., 2022)

Unconditional optimal error estimates and superconvergence analysis of energy-preserving FEM for general nonlinear Schrödinger equation with wave operator. - Dongyang Shi; Houchao Zhang (Comput. Math. Appl., 2022)

Unconditionally superconvergent error estimates of a linearized Galerkin finite element method for the nonlinear thermistor problem. - Huaijun Yang; Dongyang Shi (Adv. Comput. Math., 2023)

Unconditional superconvergence analysis for the nonlinear Bi-flux diffusion equation. - Dongyang Shi; Sihui Zhang (Appl. Math. Comput., 2023)

Convergence analysis of the Galerkin finite element method for the fourth-order Rosenau equation. - Dongyang Shi; Xu Jia (Appl. Math. Lett., 2023)

Superconvergence error analysis of an efficient mixed finite element method for time-dependent natural convection problem. - Qian Liu; Dongyang Shi (Comput. Math. Appl., 2023)

Unconditional error estimates of linearized BDF2-Galerkin FEMs for nonlinear coupled Schrödinger-Helmholtz equations. - Dongyang Shi; Houchao Zhang (Numer. Algorithms, 2023)

A linearized decoupled Crank-Nicolson FEM for Keller-Segel chemotactic model with nonlinear secretion. - Dongyang Shi; Chaoqun Li (Commun. Nonlinear Sci. Numer. Simul., 2023)

Superconvergence analysis of finite element method for nonlinear semiconductor device problem. - Dongyang Shi; Peng Jian (Comput. Math. Appl., 2023)

A novel approach of unconditional optimal error estimate of linearized and conservative Galerkin FEM for Klein-Gordon-Schrödinger equations. - Huaijun Yang; Dongyang Shi (Commun. Nonlinear Sci. Numer. Simul., 2023)

Nonconforming modified Quasi-Wilson finite element method for convection-diffusion-reaction equation. - Sihui Zhang; Xiangyu Shi; Dongyang Shi (Commun. Nonlinear Sci. Numer. Simul., 2023)

Unconditional superconvergence analysis of an energy-stable C-N fully discrete scheme for the nonlinear magnetic diffusion model with memory. - Dongyang Shi; Sihui Zhang (Appl. Math. Lett., 2023)

Unconditional superconvergence analysis of a modified nonconforming energy stable BDF2 FEM for Sobolev equations with Burgers' type nonlinearity. - Dongyang Shi; He Ma (Commun. Nonlinear Sci. Numer. Simul., 2023)

Unconditional superconvergence analysis of an energy conservation scheme with Galerkin FEM for nonlinear Benjamin-Bona-Mahony equation. - Dongyang Shi; Zhenqi Qi (Commun. Nonlinear Sci. Numer. Simul., 2023)

Unconditional superconvergence analysis of two-grid nonconforming FEMs for the fourth order nonlinear extend Fisher-Kolmogorov equation. - Lifang Pei; Chaofeng Zhang; Dongyang Shi (Appl. Math. Comput., 2024)

A high-order limiter-free arbitrary Lagrangian-Eulerian discontinuous Galerkin scheme for compressible multi-material flows. - Xiaolong Zhao; Dongyang Shi; Shicang Song; Shijun Zou (Appl. Math. Lett., 2024)

Unconditional superconvergence analysis of an energy dissipation property preserving nonconforming FEM for nonlinear BBMB equation. - Dongyang Shi; Zhenqi Qi (Comput. Appl. Math., 2024)

A leap-frog nodal discontinuous Galerkin method for Maxwell polynomial chaos Debye model. - Xixian Bai; Chunyan Niu; Dongyang Shi; Yongwei Zhang 003 (Comput. Math. Appl., 2024)

Optimal error estimates of nonconforming Wilson element for nonlinear nonlocal parabolic problems. - Dongyang Shi; Conggang Liang (Comput. Math. Appl., 2024)

Superconvergence analysis of a new stabilized nonconforming finite element method for the Stokes equations. - Dongyang Shi; Minghao Li; Qili Tang (Comput. Math. Appl., 2024)

Superconvergence of a new energy dissipation finite element scheme for nonlinear Schrödinger equation with wave operator. - Junjun Wang; Dongyang Shi; Lina Cao; Jiaxuan Pei (Comput. Math. Appl., 2024)

Nonconforming quadrilateral finite element analysis for the nonlinear Ginzburg-Landau equation. - Huazhao Xie; Dongyang Shi; Qian Liu (Comput. Math. Appl., 2024)

A high-order arbitrary Lagrangian-Eulerian discontinuous Galerkin method for compressible flows in two-dimensional Cartesian and cylindrical coordinates. - Xiaolong Zhao; Shijun Zou; Xijun Yu; Dongyang Shi; Shicang Song (Comput. Math. Appl., 2024)

Fully decoupled, linearized and stabilized finite volume method for the time-dependent incompressible MHD equations. - Xiaochen Chu; Dongyang Shi; Tong Zhang (Commun. Nonlinear Sci. Numer. Simul., 2024)

Low order nonconforming finite element methods for nuclear reactor model. - Chaoqun Li; Dongyang Shi (Commun. Nonlinear Sci. Numer. Simul., 2024)

Novel superconvergence analysis of a low order FEM for nonlinear time-fractional Joule heating problem. - Xiangyu Shi; Haijie Wang; Dongyang Shi (Commun. Nonlinear Sci. Numer. Simul., 2024)

Superconvergence error analysis of linearized semi-implicit bilinear-constant SAV finite element method for the time-dependent Navier-Stokes equations. - Huaijun Yang; Dongyang Shi (Commun. Nonlinear Sci. Numer. Simul., 2024)

Superconvergence analysis of an anisotropic nonconforming FEM for parabolic equation. - Dongyang Shi; Sihui Zhang (J. Comput. Appl. Math., 2024)

Unconditional superconvergence analysis of an energy-preserving finite element scheme for nonlinear BBM equation. - Dongyang Shi; Zhenqi Qi (Comput. Math. Appl., 2024)

Unconditional superconvergence analysis of modified finite difference streamlined diffusion method for nonlinear convection-dominated diffusion equation. - Dongyang Shi; Lingen Zhang (Comput. Math. Appl., 2024)

Optimal error estimates of an H1-Galerkin mixed finite element method for nonlinear Kirchhoff-type problem. - Yanmi Wu; Dongyang Shi (Comput. Appl. Math., 2024)

Superconvergence analysis of an H1-Galerkin mixed FEM for Klein-Gordon-Zakharov equations with power law nonlinearity. - Ran Wang; Dongyang Shi (Commun. Nonlinear Sci. Numer. Simul., 2024)

Unconditional superconvergence analysis of an energy-stable L1 scheme for coupled nonlinear time-fractional prey-predator equations with nonconforming finite element. - Dongyang Shi; Sihui Zhang (Appl. Math. Comput., 2024)

Unconditional uniform superconvergence analysis of anisotropic nonconforming energy-dissipative SAV-FEM for fourth-order singular perturbation Bi-flux diffusion equation. - Sihui Zhang; Xiangyu Shi; Dongyang Shi (Appl. Math. Lett., 2025)

Superconvergence analysis of the decoupled and linearized mixed finite element methods for unsteady incompressible MHD equations. - Xiaochen Chu; Xiangyu Shi; Dongyang Shi (Comput. Math. Appl., 2025)

Unconditional superconvergence analysis of a novel energy dissipation nonconforming Crank-Nicolson FEM for Sobolev equations with high order Burgers' type nonlinearity. - Tiantian Liang; Dongyang Shi (Comput. Math. Appl., 2025)

A new energy dissipation-preserving Crank-Nicolson type nonconforming FEM for damped wave equation with cubic nonlinearity. - Dongyang Shi; Xuemiao Xu (Comput. Math. Appl., 2025)

Quasi-uniform unconditional superconvergent error estimates of FEMs for the time-dependent singularly perturbed Bi-wave problem modeling d-wave superconductors. - Yanmi Wu; Dongyang Shi (Comput. Math. Appl., 2025)

Unconditional superconvergence analysis of low-order conforming mixed finite element method for time-dependent incompressible MHD equations. - Xiaochen Chu; Xiangyu Shi; Dongyang Shi (Commun. Nonlinear Sci. Numer. Simul., 2025)

Convergence and superconvergence analysis for a mass conservative, energy stable and linearized BDF2 scheme of the Poisson-Nernst-Planck equations. - Minghao Li; Dongyang Shi; Zhenzhen Li (Commun. Nonlinear Sci. Numer. Simul., 2025)

Superconvergence analysis and extrapolation of a BDF2 fully discrete scheme for nonlinear reaction-diffusion equations. - Conggang Liang; Dongyang Shi (Commun. Nonlinear Sci. Numer. Simul., 2025)

Superconvergence and extrapolation of a second-order θ fully discrete scheme with nonconforming FEM for degenerate nonlocal thermistor problems. - Conggang Liang; Xiangyu Shi; Dongyang Shi (Commun. Nonlinear Sci. Numer. Simul., 2025)

Superconvergence analysis of low order nonconforming finite element method for coupled nonlinear semiconductor device problem. - Xiangyu Shi; Peng Jian; Dongyang Shi (Commun. Nonlinear Sci. Numer. Simul., 2025)

Unconditional superconvergence analysis of a new energy stable nonconforming BDF2 mixed finite element method for BBM-Burgers equation. - Xuemiao Xu; Dongyang Shi (Commun. Nonlinear Sci. Numer. Simul., 2025)

A novel linearized nonconforming BDF2-FDSD method for nonlinear convection-dominated diffusion equation. - Dongyang Shi; He Ma (Comput. Appl. Math., 2025)

Unconditional superconvergence analysis of a novel structure preserving nonconforming BDF2-FEM for coupled nonlinear Schrödinger system. - Zhenqi Qi; Dongyang Shi; Xiaozhong Yang (Commun. Nonlinear Sci. Numer. Simul., 2026)