First-Order System Least Squares For Linear Elasticity: Numerical Results

First-Order System Least Squares for the Stress-Displacement Formulation: Linear Elasticity

Analysis of a Modified First-Order System Least Squares Method for Linear Elasticity with Improved Momentum Balance

A modified first-order system least squares formulation for linear elasticity, obtained by adding the antisymmetric displacement gradient in the test space, is analyzed. This approach leads to surprisingly small momentum balance error compared to standard least squares approaches. It is shown that the modified least squares formulation is well-posed and its performance is illustrated by adaptiv...

First-Order System Least Squares for the Signorini Contact Problem in Linear Elasticity

A first-order system least squares formulation for the Signorini problem modeling frictionless contact in linear elasticity is studied. In addition to the displacement field, the stress tensor is used as an independent process variable. A contact boundary term is added to the usual least squares functional in order to achieve coercivity and continuity in appropriate norms. The discrete function...

First-Order System Least Squares (FOSLS) for Spatial Linear Elasticity: Pure Traction

This paper develops first-order system least-squares (FOSLS) functionals for 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 norms of the first-order...

First-Order System Least Squares for the Stokes and Linear Elasticity Equations: Further Results

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...