Research Areas: Numerical methods of partial differential equations, computational fluid dynamics,
numerical reservoir simulation, high-precision methods for phase field model
0531-88366296
xiaolimath@sdu.edu.cn
Sep. 2013-Dec. 2018: Shandong University Ph. D
Sep. 2017-Sep. 2018: Purdue University Visiting Scholar
Jan. 2019- Dec. 2020: Xiamen University PostDoc (Co-adviser: Jie Shen)
Dec. 2020- Now: Shandong University Professor
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、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.
13、X.L. Li, and J. Shen, Efficient Linear and Unconditional Energy Stable Schemes for the Modified Phase Field Crystal Equation. SCIENCE CHINA Mathematics (2022).
14、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.
15、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.
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.
1. Jan. 2023-Dec. 2026, No.12271302 (PI, RMB 450,000, National Natural Science Foundation of China (General Program)).
2. Jan. 2020-Dec. 2022, No.11901489 (PI, RMB 250,000, National Natural Science Foundation of China (Youth Program)).
3. April. 2019-Dec. 2020, No.BX20190187. (PI, RMB 600,000, The Postdoctoral Innovation Talent Support Program)
4. May.2019-Dec.2020, No.2019M650152. (PI, RMB 120,000, China Postdoctoral Science Foundation)
