  Trimming consists of cutting away parts of a geometric domain, without
reconstructing a global parametrization (meshing). It is a widely used
operation in computer aided design, which generates meshes that are unfitted
with the described physical object. This paper develops an adaptive mesh
refinement strategy on trimmed geometries in the context of hierarchical
B-spline based isogeometric analysis. A residual a posteriori estimator of the
energy norm of the numerical approximation error is derived, in the context of
the Poisson equation. The estimator is proven to be reliable, independently of
the number of hierarchical levels and of the way the trimmed boundaries cut the
underlying mesh. Numerical experiments are performed to validate the presented
theory, and to show that the estimator's effectivity index is independent of
the size of the active part of the trimmed mesh elements.

Numerical Analysis;Numerical Analysis