Isogeometric analysis based on extended Catmull–Clark subdivision

In this paper, we propose a subdivision-based finite element method as an integration of the isogeometric analysis (IGA) framework which adopts the uniform representation for geometric modeling and finite element simulation. The finite element function space is induced from the limit form of Catmull–Clark surface subdivision containing boundary subdivision schemes which has C1 continuity everywhere. It is capable of exactly representing complex geometries with any shaped boundaries which are represented as piecewise cubic B-spline curves. It is compatible with modern Computer Aided Design (CAD) software systems. The advantage of this strategy admits quadrilateral meshes of arbitrary topology. In this work, the computational domains with planar geometries are considered. We establish the approximation properties of Catmull–Clark surface subdivision function based on the Bramble–Hilbert lemma. Numerical tests are performed through three Poisson’s equations with the Dirichlet boundary condition to corroborate the theoretical proof.