Isogeometric Analysis has been proven to be a suitable tool for the discretization of higher-order formulations describing phenomena like brittle fracture or phase separation in fluid mixtures [1, 2]. In this context, phase-field models constitute a convenient approach to model sharp interface problems, since they incorporate a continuous field variable –the field order parameter– to describe the transition between the phases, allowing for an automatic tracking of the evolution of the smooth interfaces. From a computational standpoint, phase-field models need fine meshes, at least locally, in order to accurately resolve the phase-field profile. This factor becomes particularly critical in volumetric domains, where the computational cost is a major concern. In this talk, we present an adaptive isogeometric model for volumetric phase-field problems based on the Cahn–Hilliard equation. Truncated Hierarchical B-splines (THB-splines) [3] form a basis for adaptivity that can easily be extended to higher dimensions for suitably graded hierarchical refinement and coarsening [4]. Using admissible meshing techniques to guarantee a bounded number of non-zero basis functions on each mesh element [5], we examine the potential of adaptive phase-field modeling in volumetric domains with a focus on projections and marking strategies. [1] Greco, L., Patton, A., Negri, M., Marengo, A., Perego, U., and Reali, A. (2024). Higher order phase-field modeling of brittle fracture via isogeometric analysis. Engineering with Computers, 40, 3541–3560. [2] Gómez, H., Calo, V. M., Bazilevs, Y., and Hughes, T. J. (2008). Isogeometric analysis of the Cahn–Hilliard phase-field model. Computer Methods in Applied Mechanics and Engineering, 197(49-50), 4333-4352. [3] Giannelli, C., Jüttler, B., and Speleers, H. (2012). THB-splines: The truncated basis for hierarchical splines. Computer Aided Geometric Design, 29(7), 485-498. [4] Carraturo, M., Giannelli, C., Reali, A., and Vázquez, R. (2019). Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes. Computer Methods in Applied Mechanics and Engineering, 348, 660-679. [5] Bracco, C., Giannelli, C., and Vázquez, R. (2018). Refinement algorithms for adaptive isogeometric methods with hierarchical splines. axioms, 7(3), 43.