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

The computational e$ciency of "nite elements using Chebyshev basis functions is compared with that of standard equispaced lower order (bilinear and biquadratic) and higher order (bicubic and greater) pelements in the solution of the two-dimensional scalar wave equation when using explicit time integration. All solutions use a central-di!erence-in-time temporal discretization and both consistent and lumped mass matrices are considered. The Chebyshev "nite elements are shown to possess signi"cant advantages in accuracy and in computational e$ciency with respect to p-elements for an equivalent number of nodes.