报告题目：Stability and convergence of one and second order schemes for PDE with smooth and nonsmooth initial data
时间地点：7月5日 16：00-17：00 后主楼1223
报告摘要：In this report, we consider the stability and convergence results of numerical schemes for PDEs with smooth and nonsmooth initial data. In the first part, four kinds of numerical methods based on backward Euler scheme for the Boussinesq equaitons, and the corresponding H2 stabiity results are provided. In the second part, the stability and convergence of the Crank-Nicolson/Adams-Bashforth scheme for the Burgers equation with H2 and H1 initial data are considered. The almost unconditionally stable and optimal convergence results are also provided. Finally, some numerical examples are provided to verify the established stability theory and convergence results with the smooth and nonsmooth initial data.