In this work, a method of goal-adaptive Isogeometric Analysis is proposed. We combine goal-oriented error estimation and adaptivity with hierarchical B-splines for local h-refinement. The goal-oriented error estimator is computed with a p-refined discrete dual space, which is adaptively refined alongside the primal space. This discrete dual space is proven to be a strict superset of the primal space. Hierarchical refinements are introduced in marked regions that are formed as the union of chosen coarse-level spline supports from the primal basis. We present two ways of extracting localized refinement indicators suitable for the hierarchical refinement procedure: one based on a partitioning of the dual-weighted residual into contributions of basis function supports and one based on the combination of element indicators within a basis function support. The proposed goal-oriented adaptive strategy is exemplified for the Poisson problem and a free-surface flow problem. Numerical experiments on these problems show convergence of the adaptive method with optimal rates. Furthermore, the corresponding goal-oriented error estimators are shown to be accurate, with effectivity indices in the range of 0.7-1.1.
|Number of pages||23|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Publication status||Published - 2014|
Kuru, G., Verhoosel, C. V., Zee, van der, K. G., & Brummelen, van, E. H. (2014). Goal-adaptive isogeometric analysis with hierarchical splines. Computer Methods in Applied Mechanics and Engineering, 270, 270-292. https://doi.org/10.1016/j.cma.2013.11.026