A Triangular Spectral Method for the Stokes Equations  

作　　者：Lizhen Chen Jie Shen Chuanju Xu 

机构地区：[1]School of Mathematical Sciences,Xiamen University,361005 Xiamen,China [2]Department of Mathematics,Purdue University,West Lafayette,IN,47907,USA

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2011年第2期158-179,共22页高等学校计算数学学报（英文版）

基　　金：supported by NFS grant DMS-0915066;supported by the National Natural Scheme Foundation of China(Grant number 11071203).

摘　　要：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.

关 键 词：Stokes equations triangular spectral method error analysis 

分 类 号：O17[理学—数学]