Strong form mesh-free hp-adaptive solution of linear elasticity problem

Abstract We present an algorithm for hp -adaptive collocation-based mesh-free numerical analysis of partial differential equations. Our solution procedure follows a well-established iterative solve–estimate–mark–refine paradigm. The solve phase relies on the Radial Basis Function-generated Finite Differences (RBF-FD) using point clouds generated by advancing front node positioning that supports variable density. In estimate phase, we introduce Implicit-Explicit (IMEX) error indicator, which assumes relates to difference between implicitly obtained (from phase) and local explicit re-evaluation PDE at hand higher order approximation. Based IMEX modified Texas Three Step marking strategy is used mark computational nodes h -, p - or -(de-)refinement. Finally, in refine are repositioned method locally redefined augmenting monomials according instructions from phase. performance introduced first investigated two-dimensional Peak problem further applied two- three-dimensional contact problems. show proposed indicator adequately captures global behaviour all cases considered significantly outperforms non-adaptive approach. stands another important step towards fully autonomous capable solving complex problems realistic geometries without need user intervention.