4 papers
Sampling and reconstruction of convex functions
Andrea Bonito, Albert Cohen, Wolfgang Dahmen +3
We discuss optimal recovery for classes of multivariate convex functions from given point samples, as well as the sampling numbers of these classes, corresponding to optimal sample…
A near-optimal recovery algorithm for the Stokes equations with incomplete information on the boundary conditions
Andrea Bonito, Diane Guignard
We address the problem of numerically approximating the velocity and pressure governed by the Stokes system when the boundary conditions are only partially known and thus do not un…
Alleviating missing boundary conditions in elliptic partial differential equations using interior point measurements
Andrea Bonito, Alan Demlow, Joshua M. Siktar
We consider an optimal recovery problem for the Poisson problem when the boundary data is unknown. Compensating information is provided in the form of a finite number of measuremen…
Convergence and error control of consistent PINNs for elliptic PDEs
Andrea Bonito, Ronald DeVore, Guergana Petrova +1
We provide an a priori analysis of collocation methods for solving elliptic boundary value problems. They begin with information in the form of point values of the data and utilize…