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January 2022
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Séminaire du LJLL : R. DeVore
22 mai 2015 — 14h00
Ron DeVore (Université A&M du Texas)
Data assimilation in solving parametric PDEs
Abstract
This talk is concerned with the following problem. We wish to recover the solution u(a*) to a known parametric family of PDEs at a certain parameter value a* that is unknown to us. However, we have information about the state u(a*) through some set of physical measurements which can be viewed as the application of linear functionals to u(a*). How should we merge these two pieces of information, the parametric model and the measurements, to effectively recover u(a*) ?
The parametric model is complex and the solution manifold is usually known only through a sequence of known finite dimensional spaces V_0, … ,V_n with dim(V_k) = k that are known to approximate the solution manifold to a known accuracy epsilon_k. We formulate this as an optimal recovery problem and determine the optimal solution. Our results clarify and extend the fundamental work of Maday, Patera, Penn and Yano.