研究领域

科学计算、偏微分方程数值解

间断Galerkin有限元方法

声波散射、非线性抛物界面问题、不可压缩流体的数值理论与应用

论文与著作

[1] Song, Lunji; Zhao, Shan; Liu, Kaifang A relaxed weak Galerkin method for elliptic interface problems with low regularity. Appl. Numer. Math. 128 (2018), 65–80. 

[2] Song, Lunji; Zhao, Shan Symmetric interior penalty Galerkin approaches for two-dimensional parabolic interface problems with low regularity solutions. J. Comput. Appl. Math. 330 (2018), 356–379. 

[3] Song, Lunji; Liu, Kaifang; Zhao, Shan A weak Galerkin method with an over-relaxed stabilization for low regularity elliptic problems. J. Sci. Comput. 71 (2017), no. 1, 195–218. 

[4] Song, Lunji; Yang, Chaoxia Convergence of a second-order linearized BDF-IPDG for nonlinear parabolic equations with discontinuous coefficients. J. Sci. Comput. 70 (2017), no. 2, 662–685. 

[5] Song, Lunji; Zhang, Zhimin Superconvergence property of an over-penalized discontinuous Galerkin finite element gradient recovery method. J. Comput. Phys. 299 (2015), 1004–1020. 

[6] Song, Lunji; Zhang, Zhimin Polynomial preserving recovery of an over-penalized symmetric interior penalty Galerkin method for elliptic problems. Discrete Contin. Dyn. Syst. Ser. B 20 (2015), no. 5, 1405–1426. 

[7] Song, Lunji; Gie, Gung-Min; Shiue, Ming-Cheng Interior penalty discontinuous Galerkin methods with implicit time-integration techniques for nonlinear parabolic equations. Numer. Methods Partial Differential Equations 29 (2013), no. 4, 1341–1366. 

[8] Song, Lunji; Zhang, Jing; Wang, Li-Lian A multi-domain spectral IPDG method for Helmholtz equation with high wave number. J. Comput. Math. 31 (2013), no. 2, 107–136. 

[9] Song, Lunji; Wu, Yujiang Nonlinear stability of reaction-diffusion equations using wavelet-like incremental unknowns. Appl. Numer. Math. 68 (2013), 83–107.