Lecture Content：

This report mainly discusses the stability and convergence of two types of second-order variable step-size numerical schemes for the incompressible magnetohydrodynamic equations. Scheme 1 is based on a semi-implicit scheme for handling nonlinear terms and stable lowest-order mixed finite element pairs, resulting in a coupled linear system with variable coefficients. The unconditional stability and optimal error estimates of the numerical solution are established. Scheme 2 is based on explicit handling of nonlinear terms and the ZEC technique, splitting the target problem into a series of single-variable linear equations with constant coefficients. Using the inductive hypothesis method, we provide optimal error estimates of the numerical solution under arbitrarily high-order stable mixed finite element pairs. Numerical examples verify the theoretical analysis results, and the effectiveness of the numerical schemes is validated through an adaptive algorithm.

Speaker Introduction:

Tong Zhang is a Professor at the School of Mathematics and Information Sciences, Yantai University. His main research focuses on the design of efficient numerical algorithms and their theoretical analysis for incompressible viscous fluid problems. He has published over 50 high-level academic papers, completed 6 provincial/ministerial and national-level projects as principal investigator, and currently presides over 1 General Project of Shandong Province.