刘文杰科研成果

Home Research 新建主栏目 基本信息 名称 刘文杰，哈尔滨工业大学数学学院副教授，博士生导师。2012年和2016年于哈尔滨工业大学数学学院获得硕士学位和博士学位，2016年11月至2017年11月在新加坡南洋理工大学从事博士后研究。主要研究方向为具奇异性问题的多项式逼近理论、具奇异性偏微分方程谱元法（hp有限元）的误差估计等。发表学术论文20余篇，部分论文发表于 Mathematics of Computation、 Journal of Approximation Theory、 Journal of Computational Physics和Journal of Scientific Computing 等。其研究工作获得国家自然科学基金面上项目、国家天元数学东北中心优秀青年学者奖励计划、黑龙江省优秀青年基金项目、中国博士后科学基金面上项目（一等资助）和国家自然科学基金青年项目的资助。 Experience 名称 Jan. 2022–Present, Associate Professor, School of Mathematics, Harbin Institute of Technology Apr. 2017–Dec. 2021, Lecturer, School of Mathematics, Harbin Institute of Technology Aug. 2018–Oct. 2018, Research Fellow, Nanyang Technological University Nov. 2016–Nov. 2017, Research Fellow, Nanyang Technological University Dec. 2014–Dec. 2015, Visiting scholar, Nanyang Technological University Education 名称 2012/09 - 2016/07, Doctor of Science, Computational Mathematics, Harbin Institute of Technology 2010/09- 2012/07，Master of Science, Computational Mathematics, Harbin Institute of Technology 2006/09 - 2010/07, Bachelor of Science, Information and computing science, Henan University of Science and Technology Research Interests 名称 Spectral methods and applications, hp-FEM, PDEs in domains with corners, Approximation theory Research Grants 名称 Jan. 2023–Dec. 2026, National Natural Science Foundation of China. PI: Wenjie Liu, Total amount: ￥450,000. Nov. 2017–Present, Project funded by China Postdoctoral Science Foundation. PI: Wenjie Liu, Total amount: ￥80,000. Jan. 2019–Dec. 2021, National Natural Science Foundation of China. PI: Wenjie Liu, Total amount: ￥260,000. Publications 名称 Ruiyi Xie, Boying Wu, Wenjie Liu*. Optimal error estimates for Chebyshev approximations of functions with endpoint singularities in fractional spaces. Journal of Scientific Computing. Vol. 96, 71, 2023. Wenjie Liu, Li-Lian Wang, Boying Wu. New and improved pointwise error estimates for Legendre expansions of singular functions. Submitted. 2023. Wenjie Liu, Li-Lian Wang*, Boying Wu. Bernstein-type constants for approximation of $|x|^\alpha$ by partial Fourier-Legendre and Fourier-Chebyshev sums. Journal of Approximation Theory. Vol. 291,105897. 2023. Wenjie Liu, Boying Wu*. Unconditional stability and optimal error estimates of a Crank-Nicolson Legendre-Galerkin method for the two-dimensional second-order wave equation. Numerical Algorithms. Vol 90, 137–158, 2022.pages137–158, 2022. Wenjie Liu, Li-Lian Wang*, Boying Wu. Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation. Advances in Computational Mathematics. Vol 47, 79 2021.ages137–158, 2022. Wenjie Liu, Li-Lian Wang*. Asymptotics of the generalized Gegenbauer functions of fractional degree. Journal of Approximation Theory, Vol. 253, 105378, 2020. Zhe Yu, Boying Wu, Jiebao Sun*, Wenjie Liu . A generalized-Jacobi-function spectral method for space-time fractional reaction-diffusion equations with viscosity terms. Applied Numerical Mathematics. Vol. 152, 355-378 , 2020. Wenjie Liu, Li-Lian Wang*, Shuhuang Xiang. A new spectral method using nonstandard singular basis functions for time-fractional differential equations. Communications on Applied Mathematics and Computation, Vol. 1, No. 2, 207-230, 2019. Wenjie Liu, Li-Lian Wang, Huiyuan Li. Optimal error estimates for Chebyshev approximations of functions with limited regularity in fractional Sobolev-type spaces. Mathematics of Computation, Vol. 88, 2857-2895, 2019. Jinwei Fang, Boying Wu*, Wenjie Liu. An explicit spectral collocation method using non-polynomial basis functions for the time-dependent Schrodinger equation. Mathematical Methods in the Applied Sciences. Vol. 42, No. 1, 186-203, 2019. Tianjun Wang, Yujian Jiao*, Wenjie Liu. Pseudospectral method for Fisher equation in a disk, Applied Mathematics and Computation. Vol. 343, 30-48, 2019. Chao Zhang*, Li-Lian Wang, Dongqin Gu, Wenjie Liu. On approximate inverse of Hermite and Laguerre collocation differentiation matrices and new collocation schemes in unbounded domains, Journal of Computational and Applied Mathematics, Vol. 344, 553-571, 2018. Yujian Jiao, Tianjun Wang*, Xiandong Shi, Wenjie Liu. Mixed Jacobi-Fourier spectral method for Fisher equation, Mathematical Modelling and Analysis, Vol. 23, 240-261, 2018. Wenjie Liu , Boying Wu*. High-order implicit Galerkin-Legendre spectral method for the two-dimensional Schrodinger equation, Applied Mathematics and Computation, Vol. 324, 59-68, 2018. Jinwei Fang, Boying Wu*, Wenjie Liu. An explicit spectral collocation method for the Korteweg-de Vries equation on unbounded domain, Applied Numerical Mathematics, Vol. 126, 34-52, 2018. Yingying Shan, Wenjie Liu* , Boying Wu. Space-time Legendre-Gauss-Lobatto collocation method for two-dimensional generalized sine-Gordon equation, Applied Numerical Mathematics, Vol. 122, 92-107, 2017. Chao Zhang, Wenjie Liu, Li-Lian Wang*. A new collocation scheme using non-polynomial basis functions, Journal of Scientific Computing, Vol. 70, 793-818, 2017. Wenjie Liu, Jiebao Sun, Boying Wu*. Space-time spectral method for two-dimensional semilinear parabolic equations, Mathematical Methods in the Applied Sciences, Vol. 39, No. 7, 1646-1661, 2016. Wenjie Liu, Jiebao Sun, Boying Wu*. Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equations, Numerical Algorithms, Vol. 71, No. 2, 437-455, 2016. Wenjie Liu, Jiebao Sun, Boying Wu*. Space-time spectral method for the two-dimensional generalized sine-Gordon equation, Journal of Mathematical Analysis and Applications, Vol. 427, No. 2, 787-804, 2015. Wenjie Liu, Boying Wu, Jiebao Sun*. Space-time spectral collocation method for the one-dimensional sine-Gordon equation, Numerical Methods for Partial Differential Equations, Vol. 31, No. 3, 670-690, 2015. Wenjie Liu, Boying Wu, Jiebao Sun*. Some methods to solving highly oscillatory second-order initial value problems, Journal of Computational Physics, Vol. 276, 235-251, 2014.