张进

职  称：副教授  博士生导师

办公室：长清湖校区文渊楼A区

邮  箱：[email protected]

研究方向：有限元

个人简介

张进，山东大学计算数学学士及硕士 ,西安交通大学计算数学博士。主要研究领域为奇异摄动问题的有限元方法。奇异摄动问题的解往往具有各类层，包括边界层及内部层等。为了预解这些层, 需要设计层适应网格进而得到一致收敛的数值方法。主要的学术贡献包括解决了若干个公开问题:1.建立了三角形网格上的一系列的积分不等式, 进而证明了三角形网格上的超逼近性; 证明了流线扩散有限元方法在三角形网格上的最优L2估计；2.证明了连续内罚范数严格弱于流线扩散范数，并由此得到连续内罚函数的超逼近性；3.证明了Bakhvalov网格上有限元方法的一致收敛性。 

研究兴趣

奇异摄动问题的数值算法研究；有限元方法

招生方向

硕士研究生招生专业：偏微分方程数值计算

开设课程

数值逼近、数值代数

科研项目

1.2018.1-2021.12 “奇异摄动问题有限元方法的超逼近性研究”，国家自然科学基金 (11771257)，1/6 , 57.6 万

2.2017.08–2020.06  三角形层适应网格上有限元方法的超逼近性研究, 山东省自然科学基面上项目(ZR2017MA003)， 1/6，12万

3.2018.01–2020.12  Shishkin 网格上高阶有限元方法的超逼近性研究, 山东省高校科技计划项目(J17KA169)， 1/6，3.5万

代表性成果

已发表及接收SCI论文二十篇。代表性论著：

1. Jin Zhang and Xiaowei Liu. Supercloseness of the continuous interior penalty method for singularly perturbed problems in 1D: vertex-cell interpolation. Applied Numerical Mathematics, Accepted.

2. Xiaowei Liu, Martin Stynes and Jin Zhang. Supercloseness of edge stabilization on Shishkin rectangular meshes for convection--diffusion problems with exponential layers. IMA Journal of Numerical Analysis, Accepted.

3. Xiaowei Liu and Jin Zhang. Pointwise estimates of SDFEM on Shishkin triangular meshes for problems with characteristic layers. Numerical Algorithms, 2018.

4. Jin Zhang and Xiaowei Liu. Pointwise estimates of SDFEM on Shishkin triangular meshes for problems with exponential layers. BIT Numerical Mathematics, 2018.

5. Jin Zhang and Martin Stynes.  Supercloseness of continuous interior penalty method for convection–diffusion problems with characteristic layers. Computer Methods in Applied Mechanics and Engineering, 319:549–566, 2017.

6. Jin Zhang and Xiaowei Liu. Supercloseness of the SDFEM on Shishkin triangular meshes for problems with exponential layers. Advances in Computational Mathematics, 43(4):759–775, 2017.

7. Jin Zhang and Xiaowei Liu and Min Yang. Optimal order L2 error estimate of SDFEM on Shishkin triangular meshes for singularly perturbed convection-diffusion equations. SIAM Journal on Numerical Analysis, 54(4):2060–2080, 2016.

8. Jin Zhang and Xiaowei Liu. Analysis of SDFEM on shishkin triangular meshes and hybrid meshes for problems with characteristic layers. Journal of Scientific Computing, 68(3):1299–1316, 2016.

9. Jin Zhang and Xiaowei Liu. Convergence in L2 norm of the SDFEM on a Shishkin triangular mesh for problems with characteristic layers. Applied Mathematics and Computation, 287–288:171-183, 2016.

10. Jin Zhang, and L.Q. Mei. Pointwise error estimates of the bilinear SDFEM on Shishkin meshes. Numerical Methods for Partial Differential Equations, 29(2):422–440, 2013.

11. Jin Zhang, L.Q. Mei, and Y.P. Chen. Pointwise estimates of the SDFEM for convection–diffusion problems with characteristic layers. Applied Numerical Mathematics, 64:19–34, 2013.