Recent Progress on Q^k Spectral Element Method: Accuracy, Monotonicity and Applications

：张翔雄（美国普渡大学）
：2023-12-17 09:00
：海韵园数理大楼661

报告人：张翔雄（美国普渡大学）

时  间：2023年12月17日9:00

地  点：海韵园数理大楼661

内容摘要:

The Q^k spectral element method has been a popular high order method for solving second order PDEs for nearly four decades, obtained by continuous finite element method with tenor product polynomial of degree k basis and with (k+1)-point Gauss-Lobatto quadrature. In this talk, I will present some recent results of this classical scheme, including its accuracy, monotonicity (stability), and examples of using monotonicity to construct high order accurate bound (or positivity) preserving schemes in various applications including the Allen-Cahn equation, Keller-Segel equation for chemotaxis, and especially compressible Navier-Stokes equations for high speed flows.

个人简介：

Prof. Xiangxiong Zhang is currently a professor of mathematics at Purdue University. He got his bachelor's degree in math and applied math from University of Science Technology in China in 2006, and Ph.D. in math from Brown University in 2011. From 2011 to 2014, he was a postdoctoral associate in Imaging and Computing Group, Mathematics Department, MIT. In 2014, he joined Department of Mathematics, Purdue University. His research interests include numerical PDEs, especially high order accurate schemes, and optimization algorithms, especially nonsmooth convex optimization and Riemannian optimization. He has published more than 40 articles in top-ranked international journals, including SIAM J. Numer. Anal., SIAM J. Sci. Comput., J. Comput. Phys., etc.

 

联系人：赵状