Séminaire du CIMMUL | Diane Guignard

Approximating partial differential equations without boundary conditions

Diane Guignard
Professeure
Université d’Ottawa

Résumé

We consider the problem of numerically approximating the solution of partial differential equations for which not all the input data are known. A situation of particular interest is when the boundary conditions are (partially) unknown. To alleviate this lack of knowledge, we assume to be given linear measurements of the solution. In the context of the Poisson problem with unknown boundary condition, a near optimal recovery algorithm based on the approximation of the Riesz representers of the measurement functionals in some Hilbert spaces is proposed [Binev et al. 2024]. Inherent to this algorithm is the computation of Hs, s > 1/2, inner products on the boundary of the computational domain. In this work, we borrow techniques used in the analysis of fractional diffusion problems to design and analyze a fully practical near optimal algorithm not relying on the challenging computation of Hs inner products. We start with the Poisson problem and then extend the idea to the Stokes equations.

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Le séminaire aura lieu au local 3820 du pavillon Alexandre-Vachon et en ligne.

Pour rejoindre la réunion Zoom :
https://ulaval.zoom.us/j/62680136430?pwd=eldBYjdNTG5QR2VxTTFqbVM4UGVRZz09

Meeting ID: 626 8013 6430
Passcode: 693150