Symmetric global partition polynomials for reproducing kernel elements

Abstract

The reproducing kernel element method is a numerical technique that combines finite element and meshless methods to construct shape functions of arbitrary order and continuity, yet retains the Kronecker- $$\delta $$ ? property. Central to constructing these shape functions is the construction of global partition polynomials on an element. This paper shows that asymmetric interpolations may arise due to such things as changes in the local to global node numbering and that may adversely affect the interpolation capability of the method. This issue arises due to the use of incomplete polynomials that are subsequently non-affine invariant. This paper lays out the new framework for generating general, symmetric, truly minimal and complete affine invariant global partition polynomials for triangular and tetrahedral elements. Optimal convergence rates were observed in the solution of Kirchhoff plate problems with rectangular domains.