A Legendre-Galerkin Spectral Method for Optimal Control Problems Governed by Elliptic Equations. - Yanping Chen 002; Nianyu Yi; Wenbin Liu (SIAM J. Numer. Anal., 2008)

Error estimates of mixed finite element methods for quadratic optimal control problems. - Xiaoqing Xing; Yanping Chen 002; Nianyu Yi (J. Comput. Appl. Math., 2010)

The Superconvergent Cluster Recovery Method. - Yunqing Huang; Nianyu Yi (J. Sci. Comput., 2010)

A Legendre Galerkin spectral method for optimal control problems. - Yanping Chen 002; Nianshi Xia; Nianyu Yi (J. Syst. Sci. Complex., 2011)

A Legendre-Galerkin Spectral Method for Optimal Control Problems Governed by Stokes Equations. - Yanping Chen 002; Fenglin Huang; Nianyu Yi; Wenbin Liu (SIAM J. Numer. Anal., 2011)

Recovery of normal derivatives from the piecewise L2 projection. - Yunqing Huang; Hailiang Liu; Nianyu Yi (J. Comput. Phys., 2012)

A direct discontinuous Galerkin method for the generalized Korteweg-de Vries equation: Energy conservation and boundary effect. - Nianyu Yi; Yunqing Huang; Hailiang Liu (J. Comput. Phys., 2013)

Variational discretization for optimal control problems governed by parabolic equations. - Yanping Chen 002; Tianliang Hou; Nianyu Yi (J. Syst. Sci. Complex., 2013)

Superconvergence analysis for the explicit polynomial recovery method. - Yunqing Huang; Wei Yang 018; Nianyu Yi (J. Comput. Appl. Math., 2014)

An adaptive finite volume solver for steady Euler equations with non-oscillatory k-exact reconstruction. - Guanghui Hu; Nianyu Yi (J. Comput. Phys., 2016)

A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation. - Hailiang Liu; Nianyu Yi (J. Comput. Phys., 2016)

Function, Derivative and High-Order Derivatives Recovery Methods Using the Local Symmetry Projection. - Nianyu Yi; Yunqing Huang; Wei Yang 018 (J. Sci. Comput., 2018)

Superconvergence of the Crouzeix-Raviart element for elliptic equation. - Yidan Zhang; Yunqing Huang; Nianyu Yi (Adv. Comput. Math., 2019)

A SCR-based error estimation and adaptive finite element method for the Allen-Cahn equation. - Yaoyao Chen; Yunqing Huang; Nianyu Yi (Comput. Math. Appl., 2019)

An unconditionally energy stable second order finite element method for solving the Allen-Cahn equation. - Congying Li; Yunqing Huang; Nianyu Yi (J. Comput. Appl. Math., 2019)

Superconvergent Recovery of Rectangular Edge Finite Element Approximation by Local Symmetry Projection. - Chao Wu 007; Yunqing Huang; Nianyu Yi; Jinyun Yuan (J. Sci. Comput., 2019)

A Conservative Discontinuous Galerkin Method for Nonlinear Electromagnetic Schrödinger Equations. - Nianyu Yi; Yunqing Huang; Hailiang Liu (SIAM J. Sci. Comput., 2019)

Recovery type a posteriori error estimation of adaptive finite element method for Allen-Cahn equation. - Yaoyao Chen; Yunqing Huang; Nianyu Yi (J. Comput. Appl. Math., 2020)

Adaptive direct discontinuous Galerkin method for elliptic equations. - Huihui Cao; Yunqing Huang; Nianyu Yi (Comput. Math. Appl., 2021)

An adaptive finite element method for two-dimensional elliptic equations with line Dirac sources. - Huihui Cao; Hengguang Li; Nianyu Yi; Peimeng Yin (CoRR, 2021)

Superconvergence recovery of cubic edge elements for Maxwell's equations. - Chao Wu 007; H. Zeng; Yunqing Huang; Nianyu Yi; Jinyun Yuan (J. Comput. Appl. Math., 2021)

Infinite-Time Admissibility and Exact Observability of Volterra Systems. - Jian-Hua Chen; Nianyu Yi (SIAM J. Control. Optim., 2021)

Error analysis of a decoupled, linear and stable finite element method for Cahn-Hilliard-Navier-Stokes equations. - Yaoyao Chen; Yunqing Huang; Nianyu Yi (Appl. Math. Comput., 2022)

A characteristic block-centered finite difference method for Darcy-Forchheimer compressible miscible displacement problem. - Ao Li; Jian Huang; Wei Liu; Huayi Wei; Nianyu Yi (J. Comput. Appl. Math., 2022)

A posteriori error estimates of goal-oriented adaptive finite element methods for nonlinear reaction-diffusion problems. - Fei Li 025; Nianyu Yi (J. Comput. Appl. Math., 2022)

Function and Curl Recovery for the Lowest Order Triangular Edge Element. - Chao Wu 007; Yunqing Huang; Nianyu Yi; Huayi Wei; Jinyun Yuan (J. Sci. Comput., 2022)

A mass- and energy-conserved DG method for the Schrödinger-Poisson equation. - Nianyu Yi; Hailiang Liu (Numer. Algorithms, 2022)

Analysis of a goal-oriented adaptive two-grid finite-element algorithm for semilinear elliptic problems. - Fei Li 025; Nianyu Yi (Comput. Appl. Math., 2022)

Optimal a priori error estimate of relaxation-type linear finite element method for nonlinear Schrödinger equation. - Huini Liu; Nianyu Yi (J. Comput. Appl. Math., 2023)

A conservative relaxation Crank-Nicolson finite element method for the Schrödinger-Poisson equation. - Huini Liu; Nianyu Yi; Peimeng Yin (CoRR, 2024)

A posteriori error estimators for fourth order elliptic problems with concentrated loads. - Huihui Cao; Yunqing Huang; Nianyu Yi; Peimeng Yin (CoRR, 2024)

Convergence analysis of a decoupled pressure-correction SAV-FEM for the Cahn-Hilliard-Navier-Stokes model. - Jinting Yang; Nianyu Yi (J. Comput. Appl. Math., 2024)

Recovery Type a Posteriori Error Estimation of an Adaptive Finite Element Method for Cahn-Hilliard Equation. - Yaoyao Chen; Yunqing Huang; Nianyu Yi; Peimeng Yin (J. Sci. Comput., 2024)

Optimal error estimates of a SAV-FEM for the Cahn-Hilliard-Navier-Stokes model. - Jinting Yang; Nianyu Yi; Yaoyao Chen (J. Comput. Appl. Math., 2024)

Regularity and an adaptive finite element method for elliptic equations with Dirac sources on line cracks. - Huihui Cao; Hengguang Li; Nianyu Yi; Peimeng Yin (J. Comput. Appl. Math., 2025)

A second-order dynamical low-rank mass-lumped finite element method for the Allen-Cahn equation. - Jun Yang; Nianyu Yi; Peimeng Yin (CoRR, 2025)

Neural network-enhanced hr-adaptive finite element algorithm for parabolic equations. - Jiaxiong Hao; Yunqing Huang; Nianyu Yi; Peimeng Yin (CoRR, 2025)

A linear, unconditionally stable, second order decoupled method for the nematic liquid crystal flows with SAV approach. - Ruonan Cao; Nianyu Yi (CoRR, 2025)

Enhanced gradient recovery-based a posteriori error estimator and adaptive finite element method for elliptic equations. - Ying Liu; Jingjing Xiao; Nianyu Yi; Huihui Cao (CoRR, 2025)

Rank Inspired Neural Network for solving linear partial differential equations. - Wentao Peng; Yunqing Huang; Nianyu Yi (CoRR, 2025)

Robust PDE discovery under sparse and highly noisy conditions via attention neural networks. - Shilin Zhang; Yunqing Huang; Nianyu Yi; shihan Zhang (CoRR, 2025)

AE-PINNs: Attention-enhanced physics-informed neural networks for solving elliptic interface problems. - Jiachun Zheng; Yunqing Huang; Nianyu Yi (CoRR, 2025)

Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation. - Yaoyao Chen; Hailiang Liu; Nianyu Yi; Peimeng Yin (Numer. Algorithms, 2025)

High accuracy techniques based adaptive finite element methods for elliptic PDEs. - Jingjing Xiao; Ying Liu; Nianyu Yi (J. Comput. Appl. Math., 2026)