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Our solution procedure follows a well-established iterative solve\u2013estimate\u2013mark\u2013refine paradigm. The solve phase relies on the Radial Basis Function-generated Finite Differences (RBF-FD) using point clouds generated by advancing front node positioning algorithm that supports variable node density. In the estimate phase, we introduce an Implicit-Explicit (IMEX) error indicator, which assumes that the error relates to the difference between the implicitly obtained solution (from the solve phase) and a local explicit re-evaluation of the PDE at hand using a higher order approximation. Based on the IMEX error indicator, the modified Texas Three Step marking strategy is used to mark the computational nodes for <jats:italic>h<\/jats:italic>-, <jats:italic>p<\/jats:italic>- or <jats:italic>hp<\/jats:italic>-(de-)refinement. Finally, in the refine phase, nodes are repositioned and the order of the method is locally redefined using the variable order of the augmenting monomials according to the instructions from the mark phase. The performance of the introduced <jats:italic>hp<\/jats:italic>-adaptive method is first investigated on a two-dimensional Peak problem and further applied to two- and three-dimensional contact problems. We show that the proposed IMEX error indicator adequately captures the global behaviour of the error in all cases considered and that the proposed <jats:italic>hp<\/jats:italic>-adaptive solution procedure significantly outperforms the non-adaptive approach. The proposed <jats:italic>hp<\/jats:italic>-adaptive method stands for another important step towards a fully autonomous numerical method capable of solving complex problems in realistic geometries without the need for user intervention.<\/jats:p>","DOI":"10.1007\/s00366-023-01843-6","type":"journal-article","created":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T12:01:21Z","timestamp":1685188881000},"page":"1027-1047","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Strong form mesh-free hp-adaptive solution of linear elasticity problem"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1850-412X","authenticated-orcid":false,"given":"Mitja","family":"Jan\u010di\u010d","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gregor","family":"Kosec","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,5,27]]},"reference":[{"key":"1843_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2021.102992","volume":"155","author":"BD Upadhyay","year":"2021","unstructured":"Upadhyay BD, Sonigra SS, Daxini SD (2021) Numerical analysis perspective in structural shape optimization: a review post 2000. 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