李晓丽，山东大学教授，博士生导师，入选国家高层次青年人才计划，山东省杰出青年基金获得者，山东大学杰出中青年学者。目前担任中国数学会计算数学分会常务理事以及CSIAM油水资源数值方法专委会秘书长。2013-2018年在山东大学硕博连读，期间赴美国普渡大学联合培养，博士毕业后跟随国际知名数值分析专家沈捷教授从事博后研究工作。主要研究领域为偏微分方程数值解与计算流体力学。在SIAM J. Numer. Anal., SIAM J. Sci. Comput., Math. Comp., J. Fluid Mech., Math. Mod. Meth. Appl. Sci.及J Comput. Phys.等计算数学高水平期刊上发表学术论文多篇，多次在国际国内学术会议上作邀请报告。2019年入选“博士后创新人才支持计划”，主持国家自然科学基金面上项目、重点项目子课题、青年项目等多个国家及省部级项目。
News：招收博士后及硕士博士研究生，待遇从优，在站博士后还可申领济南市生活及住房补贴，欢迎邮件咨询。
联系方式：xiaolimath@sdu.edu.cn
地址：山东大学中心校区知新楼B850
研究领域
Ø 偏微分方程数值解法、计算流体力学、油藏数值模拟、多相流保结构算法、机器学习。
科研成果
▪ D.M. Hou, X.L. Li, Z.H. Qiao, and N. Zheng, Energy stable and maximum bound principle preserving schemes for the Q-tensor flow of liquid crystals. SIAM Journal on Numerical Analysis 63(2) (2025): 824-880.
▪ X.L. Li, Y. Yu and H. Chen, A class of high-order physics-preserving schemes for thermodynamically consistent model of incompressible and immiscible two-phase flow in porous media. Journal of Computational Physics 529 (2025)：113864.
▪ X.L. Li, H. Liu and N. Zheng, Second-order, energy-stable and maximum bound principle preserving schemes for two-phase incompressible flow. Journal of Scientific Computing (2025).
▪ X.L. Li, Z.G. Liu, J. Shen and N. Zheng, On a Class of Higher-Order Fully Decoupled Schemes for the Cahn–Hilliard–Navier–Stokes System. Journal of Scientific Computing (2025).
▪ Y.J. Yan, H.X. Chen and X.L. Li, The first- and second-order energy stable, mass conservative and bounds-preserving schemes for two-phase incompressible flow with rock compressibility. Communications in Computational Physics (2025).
▪ Z.G. Liu, N. Zheng, X.L. Li, An enhanced and highly efficient semi-implicit combined Lagrange multiplier approach preserving original energy law for dissipative systems. International Journal for Numerical Methods in Engineering (2024).
▪ X.H. Wang, X. Guo, X.L. Li, A class of new linear, efficient and high-order implicit-explicit methods for the unsteady Navier-Stokes-Darcy model based on nonlinear Lions interface condition. Journal of Scientific Computing (2024).
▪ Z. Liu, Y. R. Zhang, X.L. Li, A novel energy-optimized technique of SAV-based (EOP-SAV) approaches for dissipative systems. Journal of Scientific Computing (2023).
▪ X.L. Li, W. L. Wang, and J. Shen，Stability and error analysis of IMEX SAV schemes for the magneto-hydrodynamic equations. SIAM Journal on Numerical Analysis 60(3) (2022): 1026-1054.
▪ X.L. Li, J. Shen, and Z. G. Liu, New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis. Mathematics of Computation 91(333) (2022): 141-167.
▪ X.L. Li, and J. Shen, On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows. Mathematical Models and Methods in Applied Sciences 32(03) (2022): 457-495.
▪ X.L. Li, and J. Shen, Efficient Linear and Unconditional Energy Stable Schemes for the Modified Phase Field Crystal Equation. SCIENCE CHINA Mathematics (2022).
▪ X.L. Li, and H.X. Rui，Superconvergence of MAC scheme for a Coupled Free Flow-Porous Media System with Heat Transport on Non-uniform Grids. Journal of Scientific Computing 90(3) (2022): 1-32.
▪ Z.G. Liu, and X.L. Li*, A highly efficient and accurate exponential semi-implicit scalar auxiliary variable (ESI-SAV) approach for dissipative system. Journal of Computational Physics 447 (2021)：110703.
▪ S.M. Guo, C. Li, X.L. Li, and L.Q. Mei, Energy-conserving and time-stepping-varying ESAV-Hermite-Galerkin spectral scheme for nonlocal Klein-Gordon-Schr\"{o}dinger system with fractional Laplacian in unbounded domains. Journal of Computational Physics 458 (2021)：111096.
▪ X.L. Li, and J. Shen，Error analysis of the SAV-MAC scheme for the Navier-Stokes equations. SIAM Journal on Numerical Analysis 58(5) (2020): 2465-2491.
▪ Z.G. Liu, and X.L. Li，The exponential scalar auxiliary variable (E-SAV) approach for phase field models and its explicit computing. SIAM Journal on Scientific Computing 42(3) (2020): B630-B655.
▪ X.L. Li, and J. Shen, On a SAV-MAC Scheme for the Cahn-Hilliard-Navier-Stokes Phase Field Model and its Error Analysis for the Corresponding Cahn-Hilliard-Stokes Case. Mathematical Models and Methods in Applied Sciences 30(12) (2020): 2263-2297.
▪ X.L. Li, and H.X. Rui，Superconvergence of a fully conservative finite difference method on nonuniform staggered grids for simulating wormhole propagation with the Darcy-Brinkman-Forchheimer framework. Journal of Fluid Mechanics 872 (2019): 438-471.
▪ X.L. Li, J. Shen, and H.X. Rui, Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Mathematics of Computation 88(319) (2019): 2047-2068.
▪ X.L. Li, and H.X. Rui，Superconvergence of Characteristics Marker and Cell Scheme for the Navier-Stokes Equations on Nonuniform Grids. SIAM Journal on Numerical Analysis 56(3) (2018): 1313-1337.
▪ X.L. Li, and H.X. Rui，Block-Centered Finite Difference Method for Simulating Compressible Wormhole Propagation. Journal of Scientific Computing 74(2) (2018): 1115-1145.
▪ H.X. Rui, and X.L. Li, Stability and Superconvergence of MAC Scheme for Stokes Equations on Non-uniform Grids. SIAM Journal on Numerical Analysis 55(3)(2017): 1135-1158.
▪ X.L. Li, and H.X. Rui，A Two-grid Block-centered Finite Difference Method for the Nonlinear Time-fractional Parabolic Equation. Journal of Scientific Computing 72(2) (2017)：863-891.
▪ Z.G. Liu, and X.L. Li*，A Parallel CGS Block-centered Finite Difference Method for a Nonlinear Time-fractional Parabolic Equation. Computer Methods in Applied Mechanics and Engineering 308(2016)：330-348.
