Isogeometric analysis with Powell–Sabin splines for advection–diffusion–reaction problems

By Hendrik Speleers, Carla Manni, F. Pelosi, M. Sampoli. 2012

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A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C1 rational triangular Bézier spline discretizations (2018, background): “Multiplying Equation (17) with the variation in transverse displacement δd and integrating over the entire domain Ω yields the following:”
Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed elements (2016, methodology): “This problem also exists in the IGA with unstructured meshes, such as IGA using Tsplines [37], PHT-splines [38] and Powell-Sabin splines [39].”
Isogeometric analysis: An overview and computer implementation aspects (2012, methodology): “Another direction of IGA research includes hierarchical B-splines [58, 59, 60] and unstructured Powell-Sabin splines [61].”
A locking-free model for Reissner-Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS (2015, methodology): “PS and NURPS B-splines have already been successfully employed to solve partial differential problems [30], in particular in the isogeometric environment [32, 31].”
Mathematical analysis of variational isogeometric methods* (2014, background): “Design and numerical benchmarking of isogeometric methods for advection-dominated or reaction-dominated problems can be found in Hughes et al. (2005), Buffa, Cho and Kumar (2012), Dörfel, Jüttler and Simeon (2010) and Speleers et al. (2012).”