Adaptive RBF-FD methodSlak, Jure (Avtor) Kosec, Gregor (Mentor) meshfree methodsmeshless methodsradial basis functionspartial differential equationsadaptivityrefinementnode generationfinite differencesscattered dataRadial-basis-function-generated finite differences (RBF-FD) is a method for solving partial differential equations (PDEs), which is developed into a fully automatic adaptive method during the course of this work. RBF-FD is a strong form meshless method, which means that it does not require a mesh of the problem domain, but uses only a set of nodes as the basis for the discretization. A large part of this PhD is dedicated to algorithms for meshless node generation. A new algorithm for construction of variable density meshless discretizations in arbitrary spatial dimensions is developed. It can generate points in the interior and on the boundary, has provable minimal spacing requirements, can generate $N$ points in $O(N\log N)$ time and the resulting node sets are compatible with RBF-FD. This algorithm is used as the basis of a newly proposed $h$-adaptive procedure for elliptic problems. The behavior of the procedure is analyzed on classical 2D and 3D adaptive Poisson problems. Furthermore, several contact problems from linear elasticity are solved, demonstrating successful adaptive derefinement and refinement, with the densest parts of the discretization being more than a million times denser than the coarsest. Finally, the software developed for this work and broader research is presented and published online as an open source library for solving PDEs with strong form methods.20202020-10-13 11:31:32Doktorsko delo/naloga121511sl