First-order system least squares (FOSLS) was developed in [SIAM J. Numer. Anal., 34 (1997), pp. 1727–1741; SIAM J. Numer. Anal., 35 (1998), pp. 320–335] for Stokes and elasticity equations. Several new results for these methods are obtained here. First, the inverse-norm FOSLS scheme that was introduced but not analyzed in [SIAM J. Numer. Anal., 34 (1997), pp. 1727–1741] is shown to be continuou...

Every linear planar anisotropic elastic material is equivalent, under a linear change of coordinates, to an orthotropic material. Consequently, up to linear changes of variables, there are just two "canonical" planar elastic moduli which determine the properties of any linearly elastic material. Extensions to three-dimensional elasticity and applications are indicated.

Under some generic assumptions we prove the unique continuation property for the two-dimensional inhomogeneous anisotropic elasticity system. Having established the unique continuation property, we then investigate the inverse problem of reconstructing the inclusion or cavity embedded in a plane elastic body with inhomogeneous anisotropic medium by infinitely many localized boundary measurements.

A solution for a class of two-dimensional elasticity problems concerning an isotropic body with an arc crack in its interior is obtained in terms of an integral taken around the exterior boundary of the body. A numerical procedure for solving this integral equation is outlined and numerical results for a test problem are given.

A Galerkin finite element method for the membrane elasticity problem on a meshed surface is constructed by using two-dimensional elements extended into three dimensions. The membrane finite element model is established using the intrinsic approach suggested by Delfour and Zolésio [8].

A ctitious domain method based on boundary Lagrange multipliers is proposed for linear elasticity problems in two dimensional domains. The solution of arising saddle-point problem is obtained iteratively using MINRES method with a positive deenite block diagonal preconditioner which is based on a fast direct solver for diiusion problems. Numerical experiments demonstrate the behavior of conside...