An evaluation of the cost effectiveness of Chebyshev spectral andp-finite element solutions to the scalar wave equation

Abstract

The computational efficiency of finite elements using Chebyshev basis functions is compared with that of standard equispaced lower order (bilinear and biquadratic) and higher order (bicubic and greater) p-elements in the solution of the two-dimensional scalar wave equation when using explicit time integration. All solutions use a central-difference-in-time temporal discretization and both consistent and lumped mass matrices are considered. The Chebyshev finite elements are shown to possess significant advantages in accuracy and in computational efficiency with respect to p-elements for an equivalent number of nodes. Copyright © 1999 John Wiley & Sons, Ltd.