学术论文 |
[1] Zhang, Ran; Zhai, Qilong, A weak Galerkin finite element scheme for the biharmonic equations by using polynomials of reduced order. J. Sci. Comput., 64 (2015), no. 2, 559-585. [2] Zhai, Qilong; Zhang, Ran; Wang, XiaoShen, A hybridized weak Galerkin finite element scheme for the Stokes equations. Sci. China Math., 58 (2015), no. 11, 2455-2472. [3] Wang, Ruishu; Wang, Xiaoshen; Zhai, Qilong; Zhang, Ran, A weak Galerkin finite element scheme for solving the stationary Stokes equations. J. Comput. Appl. Math., 302 (2016), 171-185. [4] Zhai, Qilong; Zhang, Ran; Mu, Lin, A new weak Galerkin finite element scheme for the Brinkman model. Commun. Comput. Phys., 19 (2016), no. 5, 1409-1434. [5] Zhang, Hongqin; Zou, Yongkui; Xu, Yingxiang;Zhai, Qilong; Yue, Hua, Weak Galerkin finite element method for second order parabolic equations. Int. J. Numer. Anal. Model., 13 (2016), no. 4, 525-544. [6] Wang, Xiuli; Zhai, Qilong; Zhang, Ran, The weak Galerkin method for solving the incompressible Brinkman flow. J. Comput. Appl. Math., 307 (2016), 13-24. [7] Zhai, Qilong; Ye, Xiu; Wang, Ruishu; Zhang, Ran, A weak Galerkin finite element scheme with boundary continuity for second-order elliptic problems, Comput. Math. Appl., 74(2017), no. 10, 2243-2252. [8] Tian, Tian; Zhai, Qilong; Zhang, Ran, A new modified weak Galerkin finite element scheme for solving the stationary Stokes equations, J. Comput. Appl. Math., 329(2018), 268-279. [9] Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran; Discrete maximum principle for the P1-P0 weak Galerkin finite element approximations. J. Comput. Phys. , 362(2018), 114-130. [10] Wang, Junping; Wang, Ruishu; Zhai, Qilong; Zhang, Ran, A Systematic Study on Weak Galerkin Finite Element Methods for Second Order Elliptic Problems, J. Sci. Comput. , 74 (2018), no. 3, 1369-1396. [11] Wang, Xiuli; Zhai, Qilong; Wang, Ruishu; Jari, Rabeea An absolutely stable weak Galerkin finite element method for the Darcy-Stokes problem. Appl. Math. Comput. , 331 (2018), 20-32. [12] Zhai, Qilong; Zhang, Ran; Malluwawadu, Nolisa; Hussain, Saqib; The weak Galerkin method for linear hyperbolic equation. Commun. Comput. Phys., 24 (2018), no. 1, 152-166. [13] Wang, Ruishu; Wang, Xiaoshen; Zhai, Qilong; Zhang, Kai; A weak Galerkin mixed finite element method for the Helmholtz equation with large wave numbers. Numer. Methods Partial Differential Equations. , 34 (2018), no. 3, 1009-1032. [14] Wang, Xiuli; Zhai, Qilong; Wang, Xiaoshen A class of weak Galerkin finite element methods for the incompressible fluid model. Adv. Appl. Math. Mech. , 11 (2019), no. 2, 360-380. [15] Wang, Zhenhua; Zhai, Qilong; Chen, Wei; Wang, Xiaoliang; Lu, Yuyuan; An, lijia; Mechanism of nonmonotonic increase in polymer size: comparison between linear and ring chains at high shear rates. Macromolecules. , (52) 2019, no. 21, 8144-8154. [16] Zhai, Qilong; Xie, Hehu; Zhang, Ran; Zhang, Zhimin; The weak Galerkin method for elliptic eigenvalue problems. Commun. Comput. Phys., 26 (2019), no. 1, 160-191. [17] Zhai, Qilong; Zhang, Ran Lower and upper bounds of Laplacian eigenvalue problem by weak Galerkin method on triangular meshes. Discrete Contin. Dyn. Syst. Ser. B., 24 (2019), no. 1, 403-413. [18] Peng, Hui; Wang, Xiuli; Zhai, Qilong; Zhang, Ran A weak Galerkin finite element method for the elliptic variational inequality. Numer. Math. Theory Methods Appl., 12 (2019), no. 3, 923-941. [19] Wang, Junping; Zhai, Qilong; Zhang, Ran; Zhang, Shangyou; A weak Galerkin finite element scheme for the Cahn-Hilliard equation. Math. Comp. , 88 (2019), no. 315, 45-71. [20] Zhai, Qilong; Xie, Hehu; Zhang, Ran; Zhang, Zhimin; Acceleration of Weak Galerkin Methods for the Laplacian Eigenvalue Problem. J. Sci. Comput., 79 (2019), no. 2, 914-934. [21] Zhang, Qianru; Kuang, Haopeng; Wang, Xiuli; Zhai, Qilong; A hybridized weak Galerkin finite element method for incompressible Stokes equations. Numer. Math. Theory Methods Appl., 12 (2019), no. 4, 1012-1038. [22] Wang, Xiuli; Zou, Yongkui; Zhai, Qilong; An effective implementation for Stokes equation by the weak Galerkin finite element method. J. Comput. Appl. Math., 370 (2020), 112586, 8 pp. [23] Wang, Xiuli; Zhai, Qilong; Zhang, Ran; Zhang, Shangyou; The weak Galerkin finite element method for solving the time-dependent integro-differential equations. Adv. Appl. Math. Mech., 12 (2020), no. 1, 164-188. [24] Zhai, Qilong; Tian, Tian; Zhang, Ran; Zhang, Shangyou; A symmetric weak Galerkin method for solving non-divergence form elliptic equations. J. Comput. Appl. Math., 372 (2020), 112693, 10 pp. [25] Peng, Hui; Zhai, Qilong; Zhang, Ran; Zhang, Shangyou; Weak Galerkin and continuous Galerkin coupled finite element methods for the Stokes-Darcy interface problem. Commun. Comput. Phys., 28 (2020), no. 3, 1147-1175. [26] Zhai, Qilong; Hu, Xiaozhe; Zhang, Ran; The shifted-inverse power weak Galerkin method for eigenvalue problems. J. Comput. Math., 38 (2020), no. 4, 606-605. [27] Zhai, Qilong; Tian, Tian; Zhang, Ran; Zhang, Shangyou A symmetric weak Galerkin method for solving non-divergence form elliptic equations. J. Comput. Appl. Math., 372 (2020), 112693, 10 pp. [28] Wang, Xiuli; Zhai, Qilong; Zhang, Ran; Zhang, Shangyou The weak Galerkin finite element method for solving the time-dependent integro-differential equations. Adv. Appl. Math. Mech., 12 (2020), no. 1, 164-188. [29] Carstensen, Carsten; Zhai, Qilong; Zhang, Ran A skeletal finite element method can compute lower eigenvalue bounds. SIAM J. Numer. Anal., 58 (2020), no. 1, 109-124. [30] Wang, Xiuli; Liu, Yuanyuan; Zhai, Qilong; The weak Galerkin finite element method for solving the time-dependent Stokes flow. Int. J. Numer. Anal. Model., 17 (2020), no. 5, 732-745. [31] Li, Hong; Zhai, Qilong; Chen, Jeff Z. Y.; Neural-network-based multistate solver for a static Schrödinger equation. Phys. Rev. A., 103 (2021), 032405. |
