Collocation-based spectral-element toolbox

Functions and example codes for a collocation spectral-element scheme (Chebyshev or Legendre)

Following in the spirit of Trefethen’s “Spectral Methods in MATLAB”, this toolbox provides concise functions and test scripts for a collocation-based spectral-element scheme.

Features include:
- choice of Chebyshev or Legendre collocation points
- flexible domain decomposition
- support for the p-element and hp-element methods of spatial refinement
- automatic barycentric interpolation
- hassle-free enforcement of global continuity across element boundaries
- hassle-free treatment of some non-rectangular domains (e.g. square duct)
- automatic reduction to the standard pseudospectral scheme, as a special case of the spectral-element method.

Example scripts include:
- linear second-order and fourth-order ODEs and PDEs
- nonlinear ODEs and PDEs
- linear eigenvalue equations (second-order and fourth-order)
- a non-conformal scheme for localized spatial refinement.