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 - <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>