h-Adaptive radial basis function finite difference method for linear elasticity problems

Abstract In 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 extended version of RBF utilizing a polynomial basis. type restricted polyharmonic splines (PHS), i.e., combination odd m -order PHS $$\phi (r)=r^m$$ ϕ ( r ) = m with additional polynomials up degree p will serve as Furthermore, new residual-based adaptive point-cloud refinement algorithm be presented its numerical performance demonstrated. computational efficiency RBF-FD approach tested means relative errors measured $$\ell _2$$ ℓ 2 -norm on several representative benchmark smooth non-smooth solutions, h -adaptive, uniform, quasi-uniform refinement.