Abstract: This mini-symposium aims to discuss and exchange ideas on current developments, mathematical analysis, and application of special methods that offer flexibility in the construction of approximation functions through the Partition of Unity (PU) concept, such as the hp-clouds, the Generalized/eXtended finite elements (GFEM/XFEM), and the PU finite elements. While contributions to all aspects of such methods are invited, some of the topics to be featured are the identification and characterizations of problems in which these special methods have a clear advantage over classical approaches; applications, including but not limited to, multi-scale, multi-physics, non-linear and time-dependent problems, simulation of failure and fracture in materials and structures; advances in a-priori and a-posteriori error analyses; stability analysis; computational implementation aspects such as numerical integration, imposition of boundary conditions, solution of the system of equations arising from this class of methods, and adaptive mesh refinement/enrichment algorithms. Additionally, contributions on innovative discretization techniques, whether mesh-based methodologies such as isogeometric analysis, smoothed finite elements, virtual element method, among others, or mesh-free methods, such as element-free Galerkin, for instance, or even coupling between some of them, would be welcome to favor interaction among different standpoints, allowing to compare the methods and to enlighten similarities and differences, encouraging novel developments to solve engineering and physical sciences problems.