Abstract
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 tri- angular 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 effi- cient 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 frame- work, allowing us to use arbitrary triangular and tetrahedral elements. AMS subject classifications: 65N35, 65N22, 65F05, 35J05
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