TY - JOUR T1 - A Triangular Spectral Method for the Stokes Equations JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 158 EP - 179 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.42s.3 UR - https://global-sci.org/intro/article_detail/nmtma/5963.html KW - Stokes equations, triangular spectral method, error analysis. AB -

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.