 Adaptive procedures for meshfree RBF unsymmetric and symmetric collocation methodsRoberto Cavoretto and Alessandra De Rossi Applied Mathematics and Computation, 2020, vol. 382, issue C Abstract: In this article we present an adaptive scheme for solving radial basis function collocation problems, which involve elliptic partial differential equations. The proposed algorithm is applied to two usual numerical methods, known as the nonsymmetric Kansa’s method and the symmetric Hermite-based approach. Basically, the refinement algorithm is firstly characterized by the use of an adaptive superimposition scheme, in which an error estimate compares two approximate solutions computed on a coarser and a finer set of collocation points, and then on a modified adaptive residual subsampling scheme. Blending these computational techniques we detect the areas that need to be refined, also having the chance to further add and/or remove adaptively collocation points. Our study is supported by several numerical results, which illustrate the performance of our iterative algorithm. Keywords: Meshfree approximation; Adaptive algorithms; Refinement schemes; Collocation methods; Partial differential equations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320303180 DOI: 10.1016/j.amc.2020.125354 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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