Pseudo-spectral least squares method for linear elasticity

The first order system least squares Legendre and Chebyshev spectral method for two dimensional space linear elasticity is investigated. The drilling rotation is defined as a new variable and the linear elasticity equation is supplemented with an auxiliary equation. The weighted L-2-norm least squares principle is applied to a stress-displacement-rotation. It is shown that the homogeneous least squares functional is equivalent to weighted H-1-norm like for stress and weighted H-1-norm for displacement and rotation. This weighted H-1-norm equivalence is lambda-uniform. Spectral convergence for both Legendre and Chebyshev approaches are given along with some numerical experiments. The generalization for three dimensional spaces is also provided. Crown Copyright (C) 2018 Published by Elsevier Ltd. All rights reserved.