Abstract
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.
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