Approximating partial differential equations without boundary conditions

Add to your list(s) Download to your calendar using vCal

• Diane Guignard (University of Ottawa)
• Monday 15 July 2024, 14:45-15:25
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact nobody.

DREW01 - Multivariate approximation, discretization, and sampling recovery

We consider the problem of numerically approximating the solution to an elliptic partial differential equation for which the boundary condition is unknown. To alleviate this missing information, we assume to be given linear measurements of the solution. In this context, a near optimal recovery algorithm based on the approximation of the Riesz representers of  the measurement functionals in some Hilbert spaces is proposed and analyzed in [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. This is joint work with Andrea Bonito.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.