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Trimming consists of cutting away parts of a geometric domain, withoutreconstructing a global parametrization (meshing). It is a widely usedoperation in computer aided design, which generates meshes that are unfittedwith the described physical object. This paper develops an adaptive meshrefinement strategy on trimmed geometries in the context of hierarchicalB-spline based isogeometric analysis. A residual a posteriori estimator of theenergy norm of the numerical approximation error is derived, in the context ofthe Poisson equation. The estimator is proven to be reliable, independently ofthe number of hierarchical levels and of the way the trimmed boundaries cut theunderlying mesh. Numerical experiments are performed to validate the presentedtheory, and to show that the estimator's effectivity index is independent ofthe size of the active part of the trimmed mesh elements.

An a posteriori error estimator for isogeometric analysis on trimmed geometries