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SUMMARY:Approximating partial differential equations without boundary cond
 itions - Diane Guignard (University of Ottawa)
DTSTART:20240715T134500Z
DTEND:20240715T142500Z
UID:TALK218131@talks.cam.ac.uk
DESCRIPTION:We consider the problem of numerically approximating the solut
 ion to an elliptic partial differential equation for which the boundary co
 ndition is unknown. To alleviate this missing information\, we assume to b
 e given linear measurements of the solution. In this context\, a near opti
 mal recovery algorithm based on the approximation of the Riesz representer
 s of &nbsp\;the measurement functionals in some Hilbert spaces is proposed
  and analyzed in [Binev et al. 2024]. Inherent to this algorithm is the co
 mputation of Hs\, s>1/2\, inner products on the boundary of the computatio
 nal domain. In this work\, we borrow techniques used in the analysis of fr
 actional diffusion problems to design and analyze a fully practical near o
 ptimal algorithm not relying on the challenging computation of Hs inner pr
 oducts. This is joint work with Andrea Bonito.
LOCATION:Seminar Room 1\, Newton Institute
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