Analysis of High-order Approximations by Spectral Interpolation Applied to One- and Two-dimensional Finite Element Method

Abstract

The implementation of high-order (spectral) approximations associated with FEM is an approach to overcome the difficulties encountered in the numerical analysis of complex problems. This paper proposes the use of the spectral finite element method, originally developed for computational fluid dynamics problems, to achieve improved solutions for these types of problems. Here, the interpolation nodes are positioned in the zeros of orthogonal polynomials (Legendre, Lobatto, or Chebychev) or equally spaced nodal bases. A comparative study between the bases in the recovery of solutions to 1D and 2D elastostatic problems are performed. Examples are evaluated, and a significant improvement is observed when the SFEM, particularly the Lobatto approach, is used in comparison to the equidistant base interpolation.

Keywords

• Spectral finite element method
• Elastostatic problem
• Orthogonal basis