An a posteriori error estimator for isogeometric analysis on trimmed geometries

Abstract

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 Poisson equation. The reliability of the estimator is proven, and the effectivity index is shown to be independent from the number of hierarchical levels and from the way the trimmed boundaries cut the underlying mesh. In particular, it is thus independent from the size of the active part of the trimmed mesh elements. Numerical experiments are performed to validate the presented theory.