Year: 2011
Numerical Mathematics: Theory, Methods and Applications, Vol. 4 (2011), Iss. 2 : pp. 158–179
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2011.42s.3
Numerical Mathematics: Theory, Methods and Applications, Vol. 4 (2011), Iss. 2 : pp. 158–179
Published online: 2011-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Stokes equations triangular spectral method error analysis.