p-refined RBF-FD solution of a Poisson problem
Numerical Analysis
2022-01-28 v1 Numerical Analysis
Abstract
Local meshless methods obtain higher convergence rates when RBF approximations are augmented with monomials up to a given order. If the order of the approximation method is spatially variable, the numerical solution is said to be p-refined. In this work, we employ RBF-FD approximation method with polyharmonic splines augmented with monomials and study the numerical properties of p-refined solutions, such as convergence orders and execution time. To fully exploit the refinement advantages, the numerical performance is studied on a Poisson problem with a strong source within the domain.
Cite
@article{arxiv.2107.03639,
title = {p-refined RBF-FD solution of a Poisson problem},
author = {Mitja Jančič and Jure Slak and Gregor Kosec},
journal= {arXiv preprint arXiv:2107.03639},
year = {2022}
}