### Abstract

Error estimates with the optimal convergence order are proved for a pressure-stabilized characteristics finite element scheme for the Oseen equations. The scheme is a combination of Lagrange–Galerkin finite element method and Brezzi–Pitkäranta’s stabilization method. The scheme maintains the advantages of both methods; (i) It is robust for convection-dominated problems and the system of linear equations to be solved is symmetric. (ii) Since the P1 finite element is employed for both velocity and pressure, the number of degrees of freedom is much smaller than that of other typical elements for the equations, e.g., P2/P1. Therefore, the scheme is efficient especially for three-dimensional problems. The theoretical convergence order is recognized by two- and three-dimensional numerical results.

Original language | English |
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Pages (from-to) | 940-955 |

Number of pages | 16 |

Journal | Journal of Scientific Computing |

Volume | 65 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2015 Feb 4 |

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### Keywords

- Error estimates
- Pressure-stabilization
- The finite element method
- The method of characteristics
- The Oseen equations

### ASJC Scopus subject areas

- Software
- Computational Theory and Mathematics
- Theoretical Computer Science
- Engineering(all)

### Cite this

*Journal of Scientific Computing*,

*65*(3), 940-955. https://doi.org/10.1007/s10915-015-9992-8

**Error Estimates of a Pressure-Stabilized Characteristics Finite Element Scheme for the Oseen Equations.** / Notsu, Hirofumi; Tabata, Masahisa.

Research output: Contribution to journal › Article

*Journal of Scientific Computing*, vol. 65, no. 3, pp. 940-955. https://doi.org/10.1007/s10915-015-9992-8

}

TY - JOUR

T1 - Error Estimates of a Pressure-Stabilized Characteristics Finite Element Scheme for the Oseen Equations

AU - Notsu, Hirofumi

AU - Tabata, Masahisa

PY - 2015/2/4

Y1 - 2015/2/4

N2 - Error estimates with the optimal convergence order are proved for a pressure-stabilized characteristics finite element scheme for the Oseen equations. The scheme is a combination of Lagrange–Galerkin finite element method and Brezzi–Pitkäranta’s stabilization method. The scheme maintains the advantages of both methods; (i) It is robust for convection-dominated problems and the system of linear equations to be solved is symmetric. (ii) Since the P1 finite element is employed for both velocity and pressure, the number of degrees of freedom is much smaller than that of other typical elements for the equations, e.g., P2/P1. Therefore, the scheme is efficient especially for three-dimensional problems. The theoretical convergence order is recognized by two- and three-dimensional numerical results.

AB - Error estimates with the optimal convergence order are proved for a pressure-stabilized characteristics finite element scheme for the Oseen equations. The scheme is a combination of Lagrange–Galerkin finite element method and Brezzi–Pitkäranta’s stabilization method. The scheme maintains the advantages of both methods; (i) It is robust for convection-dominated problems and the system of linear equations to be solved is symmetric. (ii) Since the P1 finite element is employed for both velocity and pressure, the number of degrees of freedom is much smaller than that of other typical elements for the equations, e.g., P2/P1. Therefore, the scheme is efficient especially for three-dimensional problems. The theoretical convergence order is recognized by two- and three-dimensional numerical results.

KW - Error estimates

KW - Pressure-stabilization

KW - The finite element method

KW - The method of characteristics

KW - The Oseen equations

UR - http://www.scopus.com/inward/record.url?scp=84946477514&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84946477514&partnerID=8YFLogxK

U2 - 10.1007/s10915-015-9992-8

DO - 10.1007/s10915-015-9992-8

M3 - Article

AN - SCOPUS:84946477514

VL - 65

SP - 940

EP - 955

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

SN - 0885-7474

IS - 3

ER -