Argonne National Laboratory

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.