Bracco, CesareGiannelli, CarlottaKapl, MarioVazquez, Rafael2023-06-192023-06-192023-06-192023-05-3110.1142/S0218202523500434https://infoscience.epfl.ch/handle/20.500.14299/198416WOS:000999934500001Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well suited for the representation of complex geometries, and to maintain high continuity on general domains special constructions on multi-patch geometries must be used. In this paper, we focus on adaptive isogeometric methods with hierarchical splines, and extend the construction of C-1 isogeometric spline spaces on multi-patch planar domains to the hierarchical setting. We replace the hypothesis of local linear independence for the basis of each level by a weaker assumption, which still ensures the linear independence of hierarchical splines. We also develop a refinement algorithm that guarantees that the assumption is fulfilled by C-1 splines on certain suitably graded hierarchical multi-patch mesh configurations, and prove that it has linear complexity. The performance of the adaptive method is tested by solving the Poisson and the biharmonic problems.Mathematics, AppliedMathematicsisogeometric analysisadaptivityhierarchical splinesc-1 continuitymulti-patch domainsbiharmonic problemgeometric designrefinementimplementationconstructionsubdivisionoptimalitydimensionmeshesbasestext::journal::journal article::research article