研究方向：

间断有限元方法、相场方程、高精度时间离散方法、多重网格方法

个人简介：

郭瑞晗，2014年于中国科学技术大学数学学院获计算数学博士学位，导师徐岩教授。2014年至2016年在法国进行博士后研究。2016年8月到郑州大学数学学院任教，2018年1月晋升为副教授。主要从事相场模型间断有限元算法的研究工作，主持国家自然科学面上项目、青年基金项目、河南省自然科学面上项目、河南省青年人才托举工程项目的研究。获得2016年度中国科学院优秀博士学位论文奖。

讲授课程：微积分

科研成果：

一、主持项目

1. 国家自然科学基金面上项目，12271492，2023.1-2026.12，主持

2. 河南省自然科学基金面上项目，222300420550，2022.1-2023.12，主持

3. 国家自然科学青年基金项目，11601490，2017.1-2019.12，主持

4. 河南省青年人才托举工程项目，2018HYTP011，2018.1-2020.12，主持

二、发表论文

1. Ruihan Guo and Yan Xu, Efficient solvers of discontinuous Galerkin discretization for the Cahn-Hilliard equations, Journal of Scientific Computing, 58(2014), pp.380-408.

2. Ruihan Guo, Yinhua Xia and Yan Xu, An efficient fully-discrete local discontinuous Galerkin method for the Cahn-Hilliard-Hele-Shaw system, Journal of Computational Physics, 264 (2014), pp.23-40.

3. Ruihan Guo and Yan Xu, Fast solver for the local discontinuous Galerkin discretization of the KdV type equations, Communications in Computational Physics, 17(2015), pp. 424-457.

4. Ruihan Guo, Yan Xu and Zhengfu Xu, Local discontinuous Galerkin methods for the functionalized Cahn-Hilliard equation, Journal of Scientific Computing, 63(2015), pp 913-937.

5. Ruihan Guo and Yan Xu, An efficient, unconditionally energy stable local discontinuous Galerkin scheme for the Cahn-Hilliard-Brinkman system, Journal of Computational Physics, 298(2015), pp.387-405.

6. Ruihan Guo, Liangyue Ji and Yan Xu, High order local discontinuous Galerkin methods for the Allen-Cahn equation: analysis and simulation, Journal of Computational Mathematics, 34(2016), pp.135-158.

7. Ruihan Guo and Yan Xu,  Local discontinuous Galerkin method and high order semi-implicit scheme for the phase field crystal equation, SIAM Journal on Scientific Computing, 38(2016), pp.A105-A127.

8. Ruihan Guo, Francis Filbet and Yan Xu,  Efficient high order semi-implicit time discretization and local discontinuous Galerkin methods for highly nonlinear PDEs, Journal of Scientific Computing, 68(2016), pp.1029-1054.

9. Ruihan Guo, Yinhua Xia and Yan Xu, Semi-implicit spectral deferred correction methods for highly nonlinear partial differential equations, Journal of Computational Physics, 338(2017), pp.269-284.

10. Ruihan Guo and Yan Xu, An adaptive time-stepping strategy and local discontinuous Galerkin method for the modified phase field crystal equation, Communications in Computational Physics, 24(2018), pp.123-151 .

11. Ruihan Guo and Francis Filbet, A p-adaptive local discontinuous Galerkin level set method for Willmore flow, Journal of Scientific Computing, 76(2018), pp.1148-1167.

12. Ruihan Guo and Yan Xu, Semi-implicit spectral deferred correction method based on the invariant energy quadratization approach for phase field problems, Communications in Computational Physics, 26(2019), pp.87-113.

13. Ruihan Guo and Yan Xu, Efficient, accurate and energy stable discontinuous Galerkin methods for phase field models of two-phase incompressible flows, Communications in Computational Physics, 26(2019), pp.1224-1248.

14. Ruihan and Yan Xu, High order numerical simulations for the binary fluid-surfactant system using the discontinuous Galerkin and spectral deferred correction methods, SIAM Journal on Scientific Computing, 42(2020), pp.B353–B378.

15. Lingling Zhou and Ruihan Guo*, Optimal Error Estimates of the Local Discontinuous Galerkin Method and High-order Time Discretization Scheme for the Swift-Hohenberg Equation, Journal of Scientific Computing, 93(2022),pp.46.

16. Lingling Zhou, Wenhua Chen and Ruihan Guo*,Stability and Error Estimates of a Novel Spectral Deferred Correction Time-Marching with Local Discontinuous Galerkin Methods for Parabolic Equations, Computational Methods in Applied Mathematics, 23(2023),pp.277-196.

17. Danni Zhang and Ruihan Guo*,Optimal Error Estimates of the Semi-Discrete Local Discontinuous Galerkin Method and Exponential Time Differencing Schemes for the Thin Film Epitaxy Problem without Slope Selection, Advances in Applied Mathematics and Mechanics, 15(2023),pp.545-567.

18. Ruihan Guo and Yan Xu, Semi-implicit spectral deferred correction methods based on second-order time integration schemes for nonlinear PDEs, Journal of Computational Physics, to appear.

19. Ruihan Guo and Yinhua Xia, Arbitrary high-order fully-decoupled numerical schemes for phase-field models of two-phase incompressible flows, Communications on Applied Mathematics and Computation, to appear.

教学成果：

河南省教学技能竞赛（高校理科）一等奖；河南省教学标兵