3 papers
math.NA2025
A Semi-Lagrangian scheme on embedded manifolds using generalized local polynomial reproductions
Thomas Hangelbroek, Christian Rieger, Grady B. Wright
We analyze rates of uniform convergence for a class of high-order semi-Lagrangian schemes for first-order, time-dependent partial differential equations on embedded submanifolds of…
math.NA2025
Efficiently parallelizable kernel-based multi-scale algorithm
Federico Lot, Christian Rieger
The kernel-based multi-scale method has been proven to be a powerful approximation method for scattered data approximation problems which is computationally superior to conventiona…
math.CA2024
Generalized local polynomial reproductions
Thomas Hangelbroek, Christian Rieger, Grady B. Wright
We present a general framework, treating Lipschitz domains in Riemannian manifolds, that provides conditions guaranteeing the existence of norming sets and generalized local polyno…