### Abstract

Original language | English |
---|---|

Pages (from-to) | 732-752 |

Number of pages | 21 |

Journal | SIAM Journal on Numerical Analysis |

Volume | 44 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 |

### Fingerprint

### Keywords

- Stokes equation
- Velocity-pressure-vorticity least-squares finite element method
- L2 projection
- Mass-lumping

### Cite this

*SIAM Journal on Numerical Analysis*,

*44*(2), 732-752. https://doi.org/10.1137/040613573

}

*SIAM Journal on Numerical Analysis*, vol. 44, no. 2, pp. 732-752. https://doi.org/10.1137/040613573

**L2-projected least-squares finite element methods for the Stokes equations.** / Duan, Huo-yuan; Lin, Ping; Saikrishnan, P.; Tan, Roger C. E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - L2-projected least-squares finite element methods for the Stokes equations

AU - Duan, Huo-yuan

AU - Lin, Ping

AU - Saikrishnan, P.

AU - Tan, Roger C. E.

N1 - dc.publisher: Society for Industrial and Applied Mathematics

PY - 2006

Y1 - 2006

N2 - Two new L2 least-squares (LS) finite element methods are developed for the velocity-pressure-vorticity first-order system of the Stokes problem with Dirichlet velocity boundary condition. A key feature of these new methods is that a local or almost local L2 projector is applied to the residual of the momentum equation. Such L2 projection is always defined onto the linear finite element space, no matter which finite element spaces are used for velocity-pressure-vorticity variables. Consequently, the implementation of this L2-projected LS method is almost as easy as that of the standard L2 LS method. More importantly, the former has optimal error estimates in L2-norm, with respect to both the order of approximation and the required regularity of the exact solution for velocity using equal-order interpolations and for all three variables (velocity, pressure, and vorticity) using unequal-order interpolations. Numerical experiments are given to demonstrate the theoretical results

AB - Two new L2 least-squares (LS) finite element methods are developed for the velocity-pressure-vorticity first-order system of the Stokes problem with Dirichlet velocity boundary condition. A key feature of these new methods is that a local or almost local L2 projector is applied to the residual of the momentum equation. Such L2 projection is always defined onto the linear finite element space, no matter which finite element spaces are used for velocity-pressure-vorticity variables. Consequently, the implementation of this L2-projected LS method is almost as easy as that of the standard L2 LS method. More importantly, the former has optimal error estimates in L2-norm, with respect to both the order of approximation and the required regularity of the exact solution for velocity using equal-order interpolations and for all three variables (velocity, pressure, and vorticity) using unequal-order interpolations. Numerical experiments are given to demonstrate the theoretical results

KW - Stokes equation

KW - Velocity-pressure-vorticity least-squares finite element method

KW - L2 projection

KW - Mass-lumping

U2 - 10.1137/040613573

DO - 10.1137/040613573

M3 - Article

VL - 44

SP - 732

EP - 752

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 2

ER -