Reproducing kernel element method. Part IV: Globally compatible C-n (n >= 1) triangular hierarchy

In this part of the work, a globally compatible C-n(Omega) triangular element hierarchy is constructed in the framework of reproducing kernel element method (RKEM) for arbitrary two dimensional domains. In principle, the smoothness of the globally conforming element can be made arbitrarily high (n greater than or equal to 1). The triangle interpolation field can interpolate the derivatives of an unknown function up to arbitrary mth order, (I-m), and it can reproduce complete kth order polynomials with k greater than or equal to m. This is the first interpolation hierarchical structure that has ever been constructed with both minimal degrees of freedom and higher order smoothness and continuity over discretizations of a multiple dimensional domain. The performance of the newly constructed compatible element is evaluated in solving several Kirchhoff plate problems. (C) 2004 Elsevier B.V. All rights reserved.