C1 macroelements in adaptive finite element methods

Some interesting properties of composite basis functions for C1 macroelements are investigated, including their use for constructing conforming C1 function spaces on non-conforming adaptively refined meshes. Of particular interest is the classical cubic Hsieh–Clough–Tocher 3-split triangle because of its simplicity and convergence properties in fourth-order problems, as compared with the Powell–Sabin–Heindl 6-split and 12-split triangles. A posteriori error indicators for adaptive refinement are developed. Numerical experiments demonstrate convergence rates, and adaptive refinement performance based on a simplified error indicator is tested. Extensibility to analogous three-dimensional tetrahedral elements is briefly discussed. Copyright q 2006 John Wiley & Sons, Ltd