Legendre Spectral Element Method with Nearly Incompressible Materials

TitleLegendre Spectral Element Method with Nearly Incompressible Materials
Publication TypeJournal Article
Year of Publication2011
AuthorsPeet, YV, Fischer, PF
Date Published12/2011
Other NumbersANL/MCS-P1986-1211

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.