Discrete Minus One Norm Least-Squares for the Stress Formulation of Linear Elasticity with Numerical Results

Abstract

This paper studies the discrete minus one norm least-squares methods for the stress formulation of pure displacement linear elasticity in two dimensions. The proposed least-squares functional is defined as the sum of the $L^2-$ and $H^{-1}-$norms of the residual equations weighted appropriately. The minus one norm in the functional is replaced by the discrete minus one norm and then the discrete minus one norm least-squares methods are analyzed with various numerical results focusing on the finite element accuracy and multigrid convergence performances.