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

This paper develops two first-order system least-squares (FOSLS) appro aches for the solution of the pure traction problem in planar linear e lasticity. Both are two-stage algorithms that first solve for the grad ients of displacement (which immediately yield deformation and stress) , then for the displacement itself (if desired). One approach, which u ses L-2 norms to define the FOSLS functional, is shown under certain H -2 regularity assumptions to admit optimal H-1-like performance for st andard finite element discretization and standard multigrid solution m ethods that is uniform in the Poisson ratio for all variables. The sec ond approach, which is based on H-1 norms, is shown under general assu mptions to admit optimal uniform performance for displacement flux in an L-2 norm and for displacement in an H-1 norm. These methods do not degrade as other methods generally do when the material properties app roach the incompressible limit.