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 L2-norm least squares principle is applied to a stress-displacement-rotation. It is shown that the homogeneous least squares functional is equivalent to weighted H1-norm like for stress and weighted H1-norm for displacement and rotation. This weighted H1-norm equivalence is λ-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.