This research deals with the numerical solution of multidimensional problems by spectral methods. The aim is to retain the rapid convergence of these methods that might otherwise be lost due to corner singularities in the underlying solution. The approach adopted in this research uses appropriate singular basis functions which will append the rapidly converging Chebyshev expansion for the smoother part of the solution. Corner singularities occur in a variety of problems with important engineering applications. This work should lead to increased computational ability in application areas such as driven cavity flows, cracked beams with torsion, and convection in nuclear reactors.
