Report title: Error analysis of nonlinear sub-diffusion equation under time non-uniform grid

Reporter: Professor Zhang Jiwei, School of Mathematics and Statistics, Wuhan University

Reporting time: 10:10-10:50 am, November 19, 2020

Report location: Tencent Conference ID: 892 255 965

Conference password: 1119

School contact: Lu Junliang lvjl@jlu.edu.cn

Report summary:

     The regularity of the solution of the sub-diffusion equation is relatively weak at the initial value. At the same time, for nonlinear problems, the solution may grow quickly or oscillate when it is far from the initial value. This feature requires the time grid to be non-uniform to get the best error estimate. The non-uniformity of the time grid brings great challenges to the numerical analysis. In order to obtain the stability and optimal convergence of the discrete scheme, we establish several commonly used discrete fractional Gronwall inequalities and compatible error convolution structure expressions.

Brief introduction of the speaker:

     Zhang Jiwei is a professor and doctoral supervisor at the School of Mathematics and Statistics, Wuhan University. He received his bachelor's and master's degrees from Zhengzhou University in 2003 and 2006, and his doctorate degree from Hong Kong Baptist University in 2009. Later, he did postdoctoral research at Nanyang Technological University and New York University Krona Institute. In May 2014, he worked at the Beijing Computing Science Research Center, and in November 2018, he worked at Wuhan University. The main research areas include the numerical solution of partial differential equations and non-local models, as well as the modeling and calculation of neuroscience. The main results were published in well-known journals in the industry, such as the SIAM series, Mathematics of Computation, Journal of Computational Neuroscience, Plos Comput. Bio.