Abstract
In this part of the work, a globally compatible C n(Ω) 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⩾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⩾ 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.
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