**报告题目：** Linearized and nonlinear numerical stability for nonlinear PDEs

**报告人：**Cheng Wang

**单位：**Department of Mathematics University of Massachusetts Dartmouth

**报告时间地点：**16:00-17:00, Aug. 16, 2018, M843, BISEC

The theoretical issue of numerical stability and convergence analysis for a wide class of nonlinear PDEs is discussed in this talk. For most standard numerical schemes to certain nonlinear PDEs, such as the semi-implicit schemes for the viscous Burgers’equation, a direct maximum norm analysis for the numerical solution is not available. In turn, a linearized stability analysis, based on an a-priori assumption for the numerical solution, has to be performed to make the local in time stability and convergence analysis go through. The linearized stability analysis usually requires a mild constraint between the time step and spatial grid sizes, therefore such a numerical stability is conditional. Instead, if a nonlinear numerical analysis could be directly derived, such as the convex splitting schemes for a class of gradient flows, a bound for the numerical solution becomes available, as a result of the energy stability. Therefore, the stability and convergence for these numerical schemes turn out to be unconditional.