Abstract
Abstract We investigate convergence behavior of a spectral element method based on Legendre polynomial shape functions solving linear elasticity equations for a range of Poisson's ratios of a material. We document uniform convergence rates independent of Poisson's ratio for a wide class of problems with both straight and curved elements in two and three dimensions, demonstrating locking-free properties of the spectral element method with nearly incompressible materials. We investigate computational efficiency of the current method without a preconditioner and with a simple mass-matrix preconditioner, however no attempt to optimize a choice of a preconditioner was made.
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