Linearized numerical stability for nonlinear PDEs: conditional or unconditional




 Linearized numerical stability for nonlinear PDEs: 

       conditional or unconditional

报 告 人:

Prof. Cheng Wang

University of Massachusetts Dartmouth

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地    点:


摘    要:

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. 

邀请人: 薛运华

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