A triangular spectral method for the Stokes equations is developed in this paper. The main contributions are two-fold: First of all, a spectral method using the rational approximation is constructed and analyzed for the Stokes equations in a triangular domain. The existence and uniqueness of the solution, together with an error estimate for the velocity, are proved. Secondly, a nodal basis is constructed for the efficient implementation of the method. These new basis functions enjoy the fully tensorial product property as in a tensor-produce domain. The new triangular spectral method makes it easy to treat more complex geometries in the classical spectral-element framework, allowing us to use arbitrary triangular and tetrahedral elements.
