Consistency analysis of Clough-Tocher macro-elements

Wenbo Yu

COMPUTER MODELLING & NEW TECHNOLOGIES 2014 18(12A) 338-343

Jiangxi University of Science and Technology

In this paper, we are concerned with Clough-Tocher macro-elements of any smoothness in any dimension. An n dimensional Clough-Tocher complex is a split of an n simplex by connecting its centroid with its vertices. By using the Bernstein-Bézier representation of polynomials, we first make a unified analysis of the data compatibility in bivariate macro-element and a rule is given in a general case that the underlying macro-triangle can be wildly subdivided. Then Clough-Tocher macro-elements are setup in a recursive way that the n dimensional case can be obtained based on the n − 1 dimensional case with n ≥ 3.