Y. V. Peet and P. F. Fischer, "Legendre Spectral Element Method with Nearly Incompressible Materials," Preprint ANL/MCS-P1986-1211, December 2011. [pdf]
We investigate convergence behavior of a spectral element method based on Legendre polynomial-based shape functions solving three dimensional linear elastodynamics 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, demonstrating the locking-free properties of the spectral element method with nearly incompressible materials. A similar result was previously established theoretically and computationally for hp-type finite-element methods that have similarities with and differences from the current spectral-element method. Also documented is the second-order temporal convergence of the Newmark integration scheme for time-dependent formulation for a range of Poisson's ratios.