| Full text | |
| Author(s): |
Total Authors: 4
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| Affiliation: | [1] Univ Fed Itajuba, Inst Mech Engn, 1303 BPS Ave, Itajuba, MG - Brazil
[2] Univ Estadual Campinas, Inst Math Stat & Comp Sci, Campinas, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING; v. 115, n. 4, p. 462-500, JUL 27 2018. |
| Web of Science Citations: | 0 |
| Abstract | |
In this work, we are concerned with radial basis function-generated finite difference (RBF-FD) approximations. Numerical error estimates are presented for stabilized flat Gaussians (RBF(SGA)-FD) and polyharmonic splines with supplementary polynomials (RBF(PHS)-FD) using some analytical solutions of the Poisson equation in a square domain. Both structured and unstructured point clouds are employed for evaluating the influence of cloud refinement, size of local supports, and maximal permissible degree of the polynomials in RBF(PHS)-FD. High order of accuracy was attained with both RBF(SGA)-FD and RBF(PHS)-FD especially for unstructured clouds. Absolute errors in the first and second derivatives were also estimated at all points of the domain using one of the analytical solutions. For RBF(SGA)-FD, this test showed the occurrence of improprieties of some decentered supports localized on boundary neighborhoods. This phenomenon was not observed with RBF(PHS)-FD. (AU) | |
| FAPESP's process: | 16/23374-1 - Conservation laws, balance laws and related PDEs with discontinuous and nonlocal fluxes in applied sciences: numerical analysis, theory and applications |
| Grantee: | Eduardo Cardoso de Abreu |
| Support Opportunities: | Regular Research Grants |