In context of Reproducing Kernel Hilbert Spaces (RKHS) sampling inequalities are a well-established tool to prove convergence orders: Given function on an arbitrary domain with values given on a discrete subset one can estimate Sobolev norms of that function. This concept is (mostly) independent of the concrete geometry of the domain and distribution of the points making it an interesting tool, in particular, for complex or moving geometries.
We give a survey of the theory of sampling inequalities and look at an application for kernel-based schemes in context of hyperbolic equations.

Please join in seminar room Rogowski 328 or on Zoom !