On the Limitations of Bubble Functions

Abstract

We present two examples that demonstrate no advantage in enriching a finite element subspace with bubble functions. To appear in: Computer Methods in Applied Mechanics and Engineering Preprint September 1993 Acknowledgment: The authors acknowledge the support by the National Science Foundation under Grant ASC-9217394. * Visiting Associate Professor from LNCC, Rua Lauro Muller 455, 22290 Rio de Janeiro, Brazil. i L.P.Franca and C.Farhat Preprint, September 1993 1 1. Quadratics or linears? Let us consider the problem of finding the scalar valued function u(x) defined on the unit interval and satisfying \Gammau ;xx = f on (0; 1) (1) u(0) = u(1) = 0 (2) Multiplying (1) by an arbitrary function v 2 H 1 0(\Omega\Gamma --- where H 1 0(\Omega\Gamma denotes the Hilbert space of functions satisfying (2) with square integrable value and derivative on the unit interval --- and integrating on (0; 1) by parts, yields the variational formulation: Find u 2 H 1 0 (\Omega\Gamma such that a(u; ..