Buffa, AnnalisaGantner, GregorGiannelli, CarlottaPraetorius, DirkVazquez, Rafael2022-10-242022-10-242022-10-242022-09-3010.1007/s11831-022-09752-5https://infoscience.epfl.ch/handle/20.500.14299/191580WOS:000862234000001This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of possible singularities as well as the state-of-the-art formulation of convergence and quasi-optimality of adaptive algorithms for both the finite element method and the boundary element method in the frame of isogeometric analysis.Computer Science, Interdisciplinary ApplicationsEngineering, MultidisciplinaryMathematics, Interdisciplinary ApplicationsComputer ScienceEngineeringMathematics41a1565d0765n1265n3065n3865n5065y20optimal convergence-ratesboundary-element methodsposteriori error estimationsuitable t-splineslinear independencelocal refinementhierarchical refinementpolynomial splinesshape-optimizationbezier extractiontext::journal::journal article::review article