FIRST-ORDER SYSTEM LEAST SQUARES (FOSLS) FOR PLANAR LINEAR ELASTICITY: PURE TRACTION PROBLEM.

This paper develops two first-order system least-squares (FOSLS) approaches for the solution of the pure traction problem in planar linear elasticity. Both are two-stage algorithms that first solve for the gradients of displacement (which immediately yield deformation and stress), then for the displacement itself (if desired). One approach, which uses L² norms to define the FOSLS functional, is shown under certain H² regularity assumptions to admit optimal H¹-like performance for standard finite element discretization and standard multigrid solution methods that is uniform in the Poisson ratio for all variables. The second approach, which is based on H^-1 norms, is shown under general assumptions to admit optimal uniform performance for displacement flux in an L² norm and for displacement in an HSup1; norm. These methods do not degrade as other methods generally do when the material properties approach the incompressible limit. [ABSTRACT FROM AUTHOR]