First-order system least squares (FOSLS) for spatial linear elasticity: Pure traction

This paper develops first-order system least-squares (FOSLS) functionals fo r solving the pure traction problem in three-dimensional linear elasticity It is a direct extension of an earlier paper on planar elasticity [Z. Cai, T. A. Manteuffel, S. F. McCormick, and S. V. Parter, SIAM J. Numer. Anal., 35 (1998), pp. 320-335]. Two functionals are developed, one involving L-2 n orms of the first-order system and the other involving dual norms. These fu nctionals are shown to be equivalent to appropriate product Sobolev norms, uniformly in the Poisson ratio. These results imply that standard finite el ement discretization and iterative solver techniques can be applied to obta in performance that is optimal even as the material nears the incompressibl e limit.