Tóth, BalázsBalázsTóthDüster, AlexanderAlexanderDüster2022-11-292022-11-292023-03Computational Mechanics 71 (3): 433-452 (2023-03)http://hdl.handle.net/11420/14188In this research work, the radial basis function finite difference method (RBF-FD) is further developed to solve one- and two-dimensional boundary value problems in linear elasticity. The related differentiation weights are generated by using the extended version of the RBF utilizing a polynomial basis. The type of the RBF is restricted to polyharmonic splines (PHS), i.e., a combination of the odd m-order PHS ϕ(r) = rm with additional polynomials up to degree p will serve as the basis. Furthermore, a new residual-based adaptive point-cloud refinement algorithm will be presented and its numerical performance will be demonstrated. The computational efficiency of the PHS RBF-FD approach is tested by means of the relative errors measured in ℓ2-norm on several representative benchmark problems with smooth and non-smooth solutions, using h-adaptive, uniform, and quasi-uniform point-cloud refinement.en1432-092420233433452Springerhttps://creativecommons.org/licenses/by/4.0/AdaptivityFinite differencesLinear elasticityPolyharmonic splinesPolynomialsRadial basis functionsPhysikTechnikIngenieurwissenschaftenJournal Article10.15480/882.495410.1007/s00466-022-02249-910.15480/882.4954Journal Article