The role of Bézier extraction in adaptive isogeometric analysis: Local refinement and hierarchical refinement

We present 2 adaptive refinement techniques, namely, adaptive local refinement and adaptive hierarchical refinement, for isogeometric analysis. An element‐wise point of view is adopted, exploiting Bézier extraction, which facilitates the implementation of adaptive refinement in isogeometric analysis. Locally refined and hierarchical T‐splines are used for the description of the geometry as well as for the approximation of the solution space in the analysis. The refinement is conducted with the aid of a subdivision operator, which is computed by again exploiting the Bézier extraction operator. The concept and algorithm of an element‐based adaptive isogeometric analysis are illustrated. Numerical examples are given to examine the accuracy, the convergence, and the condition number.