Truncation Error Control in Generalized Finite Element Method

In two previously published papers the writers outlined the theoretical basis for a new finite difference energy based finite element method of structural analysis. In the past, the arbitrary division separating element from difference methods has been the manner in which the integration cell was defined. In the new approach, the experience of the two methods is combined, both to clarify their similarities and to provide a new family of powerful elements. The element concept is retained as the integration cell, but contrary to common finite element practice, nodes outside of the element as well as at element vertices are included in the process of defining internal behavior. The proposed planes-stress finite element is polynomially based, and a least-squares process is used to define the polynomial coefficients. This process is equivalent to using two-dimensional Taylor Series Expansions to define the function at the ith neighboring node in terms of the behavior at the centorid (X_o, Yd_o) of the integration cell.