A superconvergence result in the RBF-FD method

Autor:	Kolar-Požun, Andrej, Jančič, Mitja, Kosec, Gregor
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	Radial Basis Function-generated Finite Differences (RBF-FD) is a meshless method that can be used to numerically solve partial differential equations. The solution procedure consists of two steps. First, the differential operator is discretised on given scattered nodes and afterwards, a global sparse matrix is assembled and inverted to obtain an approximate solution. Focusing on Polyharmonic Splines as our Radial Basis Functions (RBFs) of choice, appropriately augmented with monomials, it is well known that the truncation error of the differential operator approximation is determined by the degree of monomial augmentation. Naively, one might think that the solution error will have the same order of convergence. We present a superconvergence result that shows otherwise - for some augmentation degrees, order of convergence is higher than expected. Comment: 6 pages, 4 figures. A preprint for the Eurotherm 2024 conference
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.03393 Zobrazit plný text záznamu View this record from Arxiv