Abstract

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.