2017年11月20日 |  English version
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Linearized numerical stability for nonlinear PDEs: conditional or unconditional

报告题目: Linearized numerical stability for nonlinear PDEs: conditional or unconditional

报告人:Wang Cheng教授,University of Massachusetts

报告时间:2017年9月2日(周六)10:00

报告地点:行健楼学术报告室526

Abstract: 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. If the functional norm associated with a-priori assumption is stronger than the convergence estimate norm, the linearized stability analysis usually requires a mild constraint between the time step and spatial grid sizes. In this case, such a numerical stability is conditional. Instead, if the a-priori assumption bound for the numerical solution is associated with the same functional norm as the convergence estimate norm, the linearized stability becomes unconditional, for a fixed final time. A few examples of both cases will be presented and analyzed in the talk. 
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