微分方程团队成员—刘晓薇

发布者:hhxx发布时间:2023-12-29浏览次数:63

   刘晓薇,教授,硕士生导师,于20062014年分别获华南师范大学和同济大学数学硕士、博士学位。主要兴趣:(1)奇异摄动问题的有限元方法及分析;(2)非线性偏微分方程解的定性研究。主持国家自然科学青年基金1项,山东省自然科学基金面上项目2项,承担国家自然科学基金面上项目1项,在SIAM Journal on Numerical AnalysisIMA Journal of Numerical AnalysisJournal of Differential Equations等国际学术期刊发表SCI论文四十余篇,获山东省高等学校自然科学技术奖二等奖2项。

 

承担科研项目情况

1、山东省自然科学基金面上项目,ZR2021MA004、反应扩散方程组Robin边值问题解的定性分析及数值算法研究、2022.1-2024.1210万元、在研、主持。

2、国家自然科学基金面上项目,11771257奇异摄动问题有限元方法的超逼近性研究、2018.01–2021.1248万元、结题、参与

3、国家自然科学青年基金,11601251反应扩散方程Robin边值问题解的渐近行为研究2017/01-2019/1219万元、结题、主持。

4、山东省自然科学基金面上项目,ZR2016AM13、带Robin边界条件和自由边界条件的反应扩散方程研究、2016/11-2019/0612万元、结题、主持。

5山东省高等学校科技计划项目J16LI10外来物种入侵的反应扩散模型研究2016/08-2019/085万元、结题、主持。

 

代表性论文
1Xiaowei Liu, Min Yang, Jin Zhang, Supercloseness of weak Galerkin method for a singularly perturbed convection–diffusion problem in 2DJournal of Computational and Applied Mathematics, 2024, 436: 115404.
2Xiaowei LiuJin ZhangUniform convergence of optimal order for a finite element method on a Bakhvalov-type mesh for a singularly perturbed convection diffusion equation with parabolic layers, Numerical Algorithms, 2023, 94: 459–478.

3Xiaowei LiuJin ZhangSupercloseness of weak Galerkin method on Bakhvalov type mesh for a singularly perturbed problem in 1D, Numerical Algorithms, 2023, 93: 367–395.
4Xiaowei LiuJin ZhangSupercloseness and post-processing of finite element method in a balanced norm for singularly perturbed reaction-diffusion equationComputers & Mathematics with Applications, 2023, 142: 1-8.

5Xiaowei LiuMin YangError estimations in the balanced norm of finite element method on Bakhvalov–Shishkin triangular mesh for reaction–diusion problemsApplied Mathematics Letters, 2022, 123: 107523.

6Xiaowei Liu, Jin Zhang, Supercloseness of linear streamline diffusion finite element method on Bakhvalov-type mesh for singularly perturbed convection diffusion equation in 1D, Applied Mathematics and Computation, 2022, 430127258. 

7Xiaowei LiuJin ZhangUniform supercloseness of Galerkin finite element method for convection-diffusion problems with characteristic layersComputers & Mathematics with Applications2018, 75: 444-458.

8Xiaowei LiuJin ZhangPointwise estimates of SDFEM on Shishkin triangular meshes for problems with characteristic layersNumerical Algorithms201878:465-483.

9Xiaowei LiuMartin Stynes, Jin ZhangSupercloseness of edge stabilization on Shishkin rectangular meshes for convection-diffusion problems with exponential layersIMA Journal of Numerical Analysis2018, 38: 2105–2122.

10Xiaowei LiuJin ZhangThe transition speed of reaction-diffusion problems with Robin and free boundary conditions, Applied Mathematics Letters, 2018, 76:135-141.

11Xiaowei LiuJin ZhangAsymptotic behaviors of radially symmetric solutions to diffusion problems with Robin boundary condition in exterior domain, Nonlinear Analysis: Real World Applications, 201839: 1-13.

12Xiaowei LiuJin ZhangGalerkin finite element methods for convection–diffusion problems with exponential layers on Shishkin triangular meshes and hybrid meshes, Applied Mathematics and Computation, 2017, 307244-256.

13Xiaowei LiuJin ZhangAnalysis of the SDFEM in a streamline diffusion norm for singularly perturbed convection diffusion problems, Applied Mathematics Letters, 2017,69:61-66.

14Xiaowei LiuJin ZhangAsymptotic behavior of solutions of a reaction diffusion equation with inhomogeneous Robin boundary condition and free boundary conditionNonlinear Analysis: Real World Applications, 2016, 28126-139.
 15
Jin ZhangXiaowei LiuMin YangOptimal order L^2 error estimate of SDFEM on Shishkin triangular meshes for singularly perturbed convection diffusion equationsSIAM Journal on Numerical Analysis, 2016, 54(4): 2060-2080.

16Xiaowei Liu, Bendong Lou, On a reaction–diffusion equation with Robin and free boundary conditions, Journal of Differential Equations, 2015, 259 (2): 423-453.

17Xiaowei Liu, Jin Zhang, Analysis of the SDFEM for convection-diffusion problems with characteristic layers, Applied Mathematics and Computation, 2015, 262326-334.

18Xiaowei Liu, Bendong Lou, Asymptotic Behavior of Solutions to Diffusion Problems with Robin and Free Boundary Conditions, Mathematical Modelling of Natural Phenomena, 2013, 8(3): 18-32.