General complete Lagrange family for the cube in finite element interpolations Original Research Article

In this paper, we have first derived the interpolation polynomials for the General Serendipity elements which allow arbitrarily placed nodes along the edges. We have then presented a method to determine the interpolation functions for the General Complete Lagrange elements which allow arbitrarily placed nodes. Explicit expressions for interpolation functions of the Serendipity and Complete Lagrange family elements which allow uniform spacing of nodes over the element domain are derived for elements of orders 4–10. We have also modified the Shape functions of Complete Lagrange family so that they can correctly interpolate the complete polynomial in the global space for angular distortions.