On the structure of function spaces in optimal recovery of point functionals for ENO-schemes by radial basis functions
A general theory of optimal recovery of linear functionals in native spaces of radial basis functions is developed and applied to the recovery of Dirac functionals from call averages in the reconstruction step of finite volume essentially non-oscillatory (ENO) schemes for hyperbolic conservation laws. Those native spaces are characterized, conditions on the recovery problem to be uniquely solvable. Numerical experiments show that radial recovery is indeed superior compared with classical polynomial recovery.
finite volume essentially non-oscillatory schemes
scientific article; zbMATH DE number 932014