Enhancing isogeometric analysis by a finite element-based local refinement strategy

Abstract While isogeometric analysis has the potential to close the gap between computer aided design and finite element methods, the underlying structure of NURBS (non-uniform rational B -splines) is a weakness when it comes to local refinement. We propose a hybrid method that combines a globally C 1 -continuous, piecewise polynomial finite element basis with rational NURBS-mappings in such a way that an isoparametric setting and exact geometry representation are preserved. We define this basis over T -meshes with a hierarchical structure that allows locally restricted refinement. Combined with a state-of-the-art a posteriori error estimator, we present an adaptive refinement procedure. This concept is successfully demonstrated with the Laplace equation, advection–diffusion problems and linear elasticity problems.

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