@Article{NMTMA-4-158,
author = {Lizhen Chen, Jie Shen and Chuanju Xu},
title = {A Triangular Spectral Method for the Stokes Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2011},
volume = {4},
number = {2},
pages = {158--179},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2011.42s.3},
url = {http://global-sci.org/intro/article_detail/nmtma/5963.html}
}