Linearized and nonlinear numerical stability
主 题: Linearized and nonlinear numerical stability
报告人: 王成(邵嗣烘) (University of Massachusetts Dartmouth)
时 间: 2016-07-29 10:00-11:00
地 点: 理科一号楼 1418
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.