Error indicators and refinement strategies for solving Poisson problems through a RBF partition of unity collocation scheme

Roberto Cavoretto and Alessandra De Rossi

Applied Mathematics and Computation, 2020, vol. 369, issue C

Abstract: In this article adaptive refinement algorithms are presented to solve Poisson problems by a radial basis function partition of unity (RBF-PU) collocation scheme. Since in this context the problem of constructing an adaptive discretization method to be really effective is still open, we propose some error indicators and refinement strategies, so that each of these two essential ingredients takes advantage of the potentiality of the other one. More precisely, the refinement techniques coupled with a local error indicator is an ad-hoc strategy for the RBF-PU method. The resulting scheme turns out to be flexible and the use of efficient searching procedures enables us a fast detection of the regions that adaptively need the addition/removal of points. Several numerical experiments and applications support our study by illustrating the performance of our adaptive algorithms.

Keywords: Meshfree methods; Radial basis function collocation; Refinement schemes; Adaptive algorithms; Elliptic partial differential equations (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308161

DOI: 10.1016/j.amc.2019.124824

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