Close Search Advanced
Journals
Resources
About Us
Open Access

A Triangular Spectral Method for the Stokes Equations

A Triangular Spectral Method for the Stokes Equations
Preview
Add to basket

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

  1. Efficient SVV stabilized triangular spectral element methods for incompressible flows of high Reynolds numbers

    Chen, Lizhen | Tang, Tao | Xu, Chuanju

    Advances in Aerodynamics, Vol. 4 (2022), Iss. 1

    https://doi.org/10.1186/s42774-021-00090-x [Citations: 0]

  2. Stokes Eigenmodes on two-dimensional regular polygons

    Lallemand, Pierre | Chen, Lizhen | Labrosse, Gérard | Luo, Li–Shi

    Computers & Fluids, Vol. 228 (2021), Iss. P.105069

    https://doi.org/10.1016/j.compfluid.2021.105069 [Citations: 0]

  3. A spectral method for triangular prism

    Li, Jingliang | Ma, Heping | Qin, Yonghui | Zhang, Shuaiyin

    Applied Numerical Mathematics, Vol. 129 (2018), Iss. P.26

    https://doi.org/10.1016/j.apnum.2018.02.009 [Citations: 2]

  4. A triangular spectral method for the Stokes eigenvalue problem by the stream function formulation

    Cao, Junying | Wang, Ziqiang | Chen, Lizhen

    Numerical Methods for Partial Differential Equations, Vol. 34 (2018), Iss. 3 P.825

    https://doi.org/10.1002/num.22229 [Citations: 2]

  5. On the Inf-Sup Constant of a Triangular Spectral Method for the Stokes Equations

    Su, Yanhui | Chen, Lizhen | Li, Xianjuan | Xu, Chuanju

    Computational Methods in Applied Mathematics, Vol. 16 (2016), Iss. 3 P.507

    https://doi.org/10.1515/cmam-2016-0011 [Citations: 9]

  6. A triangular spectral element method for elliptic and Stokes problems

    Li, Jingliang | Ma, Heping | Li, Huiyuan

    Applied Mathematics and Computation, Vol. 321 (2018), Iss. P.195

    https://doi.org/10.1016/j.amc.2017.10.025 [Citations: 2]

  7. SPECTRAL-GALERKIN APPROXIMATION BASED ON REDUCED ORDER SCHEME FOR FOURTH ORDER EQUATION AND ITS EIGENVALUE PROBLEM WITH SIMPLY SUPPORTED PLATE BOUNDARY CONDITIONS

    Wang, Yuanlu | Jiang, Jiantao | An, Jing

    Journal of Applied Analysis & Computation, Vol. 14 (2024), Iss. 1 P.61

    https://doi.org/10.11948/20230018 [Citations: 0]

  8. Least Squares Triangular Legendre Galerkin with Numerical Integral Method for Elliptic Equations

    严, 梓奇

    Advances in Applied Mathematics, Vol. 08 (2019), Iss. 02 P.235

    https://doi.org/10.12677/AAM.2019.82027 [Citations: 0]

  9. A High-Order Lower-Triangular Pseudo-Mass Matrix for Explicit Time Advancement of hp Triangular Finite Element Methods

    Appleton, Jay Miles | Helenbrook, Brian T.

    SIAM Journal on Numerical Analysis, Vol. 59 (2021), Iss. 3 P.1618

    https://doi.org/10.1137/19M1268471 [Citations: 0]

  10. Spectrally accurate Stokes eigen-modes on isosceles triangles

    Chen, Lizhen | Labrosse, Gérard | Lallemand, Pierre | Luo, Li-Shi

    Computers & Fluids, Vol. 132 (2016), Iss. P.1

    https://doi.org/10.1016/j.compfluid.2016.03.004 [Citations: 6]

  11. Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations

    Song, Fangying | Xu, Chuanju | Karniadakis, George Em

    SIAM Journal on Scientific Computing, Vol. 39 (2017), Iss. 4 P.A1320

    https://doi.org/10.1137/16M1078197 [Citations: 41]