<i>C</i>¹ macroelements in adaptive finite element methods

Abstract

Abstract Some interesting properties of composite basis functions for C 1 macroelements are investigated, including their use for constructing conforming C 1 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 © 2006 John Wiley &amp; Sons, Ltd.