Adaptive procedures for meshfree RBF unsymmetric and symmetric collocation methods

•Adaptive methods for elliptic PDEs.•RBF collocation schemes.•Error indicators for meshless methods. 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 u...

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Bibliographic Details
Published in:Applied mathematics and computation 2020-10, Vol.382, p.125354, Article 125354
Main Authors: Cavoretto, Roberto, De Rossi, Alessandra
Format: Article
Language:English
Subjects:
Adaptive algorithms
Collocation methods
Meshfree approximation
Partial differential equations
Refinement schemes
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Summary:•Adaptive methods for elliptic PDEs.•RBF collocation schemes.•Error indicators for meshless methods. 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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2020.125354