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A Triangular Spectral Method for the Stokes Equations

Published online by Cambridge University Press:  28 May 2015

Lizhen Chen ,
Jie Shen  and
Chuanju Xu
Lizhen Chen
Affiliation:
School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China
Jie Shen*
Affiliation:
School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA
Chuanju Xu*
Affiliation:
School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China
*
Corresponding author.Email address:shen@math.purdue.edu
Corresponding author.Email address:cjxu@xmu.edu.cn
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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 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.

Keywords

65N3565N2265F0535J05Stokes equationstriangular spectral methoderror analysis
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 2 , May 2011 , pp. 158 - 179
Copyright
Copyright © Global Science Press Limited 2011

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