李晓丽，山东大学数学学院教授、博士生导师，山东大学杰出中青年学者。
研究方向为偏微分方程数值解法与计算流体力学。
联系方式：xiaolimath@sdu.edu.cn
地址：山东大学中心校区知新楼B850
教育背景
2013.09 - 2018.12 山东大学 计算数学 导师 芮洪兴教授 硕博连读
2017.09 - 2018.09 普渡大学 计算数学 导师 沈捷教授 博士联合培养
2009.09 - 2013.07 山东师范大学 信息与计算科学 学士学位
工作经历
2022.01-至今 山东大学 计算数学 教授
2020.12 - 2021.12 山东大学 计算数学 研究员
2019.01 - 2020.12 厦门大学 计算数学 合作导师 沈捷教授 博士后／特任副研究员
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、相场模型高精度算法
项目经历
Ø国家自然科学基金面上项目12271302（2023.01-2026.12）主持 在研
Ø山东大学齐鲁青年学者 (2022.01-2026.12) 主持 在研
Ø国家自然科学青年基金11901489（2020.01-2022.12）主持 已结题
Ø博士后创新人才支持计划BX20190187（2019.04-2020.12）主持 已结题
Ø中国博士后科学基金面上一等资助2019M650152（2019.05-2020.12）主持 已结题
Ø国家自然科学重点项目12131014（2022.01-2026.12）3/32 在研
科研成果
1、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.
2、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.
3、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.
4、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.
5、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.
6、 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.
7、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.
8、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.
9、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.
10、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.
11、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.
12、X.L. Li, and J. Shen, Efficient Linear and Unconditional Energy Stable Schemes for the Modified Phase Field Crystal Equation. SCIENCE CHINA Mathematics (2021).
13、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.
14、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.
15、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.
16、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.
17、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.
18、Z.G. Liu, and X.L. Li，A Fast Finite Difference Method for a Continuous Static Linear Bond-Based Peridynamics Model of Mechanics. Journal of Scientific Computing 72 (4) (2018): 728-742.
19、X.L. Li, and J. Shen, Stability and Error Estimates of the SAV Fourier-spectral Method for the Phase Field Crystal Equation. Advances in Computational Mathematics 46(8) (2020): 1-20.
20、X.L. Li, Yanping Chen, and Chuanjun Chen, An improved two-grid technique for the nonlinear time-fractional parabolic equation based on the block-centered finite difference method. Journal of Computational Mathematics (2021).
21、X.L. Li, and H.X. Rui, Block-centered Finite Difference Methods for Non-Fickian Flow in Porous Media. Journal of Computational Mathematics 36(4) (2018): 492-516.
22、Z.G. Liu, and X.L. Li*，Efficient modified techniques of invariant energy quadratization approach for gradient flows. Applied Mathematics Letters 98 (2019): 206-214.
23、X.L. Li, and H.X. Rui，A Two-grid Block-centered Finite Difference Method for Nonlinear Non-Fickian Flow Model. Applied Mathematics and Computation 281（2016）：300-313.
24、X.L. Li, and H.X. Rui, Characteristic Block-centered Finite Difference Method for Compressible Miscible Displacement in Porous Media. Applied Mathematics and Computation 314 (2017): 391-407.
25、X.L. Li, and H.X. Rui, Characteristic Block-centered Finite Difference Method for Simulating Incompressible Wormhole Propagation. Computers & Mathematics with Applications 73(10)（2017）：2171-2190.
26、 Z.G. Liu, and X.L. Li*，Step-by-step solving schemes based on scalar auxiliary variable and invariant energy quadratization approaches for gradient flows. Numerical Algorithms （2020）.
27、X.L. Li, and H.X. Rui，Two Temporal Second Order H^1-Galerkin Mixed Finite Element Schemes for Distributed-Order Fractional Sub-Diffusion Equations. Numerical Algorithms 79(4)（2018）：1107-1130.
28、X.L. Li, H.X. Rui, and Z.G. Liu, Two Alternating Direction Implicit Spectral Methods for Two-dimensional Distributed-order Differential Equation. Numerical Algorithms 82(1)（2019）321-347.
29、X.L. Li, H.X. Rui, and S.S. Chen, A Fully Conservative Block-centered Finite Difference Method for Simulating Darcy-Forchheimer Compressible Wormhole Propagation. Numerical Algorithms 82(2)（2019）451-478.
30、X.L. Li, and H.X. Rui, Stability and convergence based on the finite difference method for the nonlinear fractional cable equation on non-uniform staggered grids. Applied Numerical Mathematics 152 (2020): 403-412.
31、X.L. Li, and H.X. Rui, A High-order Fully Conservative Block-centered Finite Difference Method for the Time-fractional Advection–dispersion Equation. Applied Numerical Mathematics 124 (2018): 89-109.
32、X.L. Li, and H.X. Rui，A Block-centered Finite Difference Method for the Distributed-order Time-fractional Diffusion-wave Equation. Applied Numerical Mathematics 131 (2018): 123-139.
33、X.L. Li, H.X. Rui, and Z.G. Liu, A Block-Centered Finite Difference Method for Fractional Cattaneo Equation. Numerical Methods for Partial Differential Equations 34(1) (2018): 296-316.
34、X.L. Li, and H.X. Rui, A fully conservative block-centered finite difference method for Darcy-Forchheimer incompressible miscible displacement problem. Numerical Methods for Partial Differential Equations 22(1) (2020): 66-85.
35、N. Zheng, and X.L. Li*, Energy Stability and Convergence of the SAV Fourier-spectral Method for the Viscous Cahn-Hilliard Equation. Numerical Methods for Partial Differential Equations 36(5) (2020): 998-1011.
36、Z.G. Liu, X.L. Li*, and J. Huang, Accurate and efficient algorithms with unconditional energy stability for the time fractional Cahn–Hilliard and Allen–Cahn equations. Numerical Methods for Partial Differential Equations (2021).
37、X.L. Li, and H.X. Rui, Stability and Superconvergence of MAC Schemes for Time Dependent Stokes Equations on Nonuniform Grids. Journal of Mathematical Analysis and Applications 466(2) (2018): 1499-1524.
38、X.L. Li, and H.X. Rui, Characteristic Block-centred Finite Difference Methods for Nonlinear Convection
Dominated Diffusion Equation. International Journal of Computer Mathematics 94（2017）：386-404.
