Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning

A new Chebyshev pseudospectral algorithm for second-order elliptic equations using finite element preconditioning is proposed and tested on various problems. Bilinear and biquadratic Lagrange elements are considered as well as bicubic Hermite elements. The numerical results show that bilinear elements produce spectral accuracy with the minimum computational work. L-shaped regions are treated by a subdomain approach.