On Certain Approximations in the Finite-Element Method

Abstract

Approximations made outside of the variational principle used in the finite-element method are examined for a restricted problem in elasticity. They are shown to be rigorous from the standpoint of a generalized variational principle in which Lagrange multipliers are utilized. The convergence of the Ritz solution to the exact solution is demonstrated. The bound is shown to be a function of the quality of both the displacement functions and other approximate functions in the analysis.