### Abstract

An a posteriori error estimate is derived and analyzed for the mini-element discretization of the Stokes equations. The estimate is based on the solution of a local Stokes problem in each element of the finite element mesh, using spaces of quadratic bump functions for both velocity and pressure errors. This results in solving a 9 × 9 system which reduces to two easily invertible 3 × 3 systems. Comparisons with other estimates based on a Petrov-Galerkin solution are used in this analysis, which shows that it provides a reasonable approximation of the actual discretization error. Numerical experiments clearly show the efficiency of such an estimate in the solution of self-adaptive mesh refinement procedures.

Original language | English (US) |
---|---|

Pages (from-to) | 591-623 |

Number of pages | 33 |

Journal | SIAM Journal on Numerical Analysis |

Volume | 28 |

Issue number | 3 |

State | Published - Jun 1991 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics
- Computational Mathematics

### Cite this

*SIAM Journal on Numerical Analysis*,

*28*(3), 591-623.

**Posteriori error estimates for the Stokes problem.** / Bank, Randolph E.; Welfert, Bruno.

Research output: Contribution to journal › Article

*SIAM Journal on Numerical Analysis*, vol. 28, no. 3, pp. 591-623.

}

TY - JOUR

T1 - Posteriori error estimates for the Stokes problem

AU - Bank, Randolph E.

AU - Welfert, Bruno

PY - 1991/6

Y1 - 1991/6

N2 - An a posteriori error estimate is derived and analyzed for the mini-element discretization of the Stokes equations. The estimate is based on the solution of a local Stokes problem in each element of the finite element mesh, using spaces of quadratic bump functions for both velocity and pressure errors. This results in solving a 9 × 9 system which reduces to two easily invertible 3 × 3 systems. Comparisons with other estimates based on a Petrov-Galerkin solution are used in this analysis, which shows that it provides a reasonable approximation of the actual discretization error. Numerical experiments clearly show the efficiency of such an estimate in the solution of self-adaptive mesh refinement procedures.

AB - An a posteriori error estimate is derived and analyzed for the mini-element discretization of the Stokes equations. The estimate is based on the solution of a local Stokes problem in each element of the finite element mesh, using spaces of quadratic bump functions for both velocity and pressure errors. This results in solving a 9 × 9 system which reduces to two easily invertible 3 × 3 systems. Comparisons with other estimates based on a Petrov-Galerkin solution are used in this analysis, which shows that it provides a reasonable approximation of the actual discretization error. Numerical experiments clearly show the efficiency of such an estimate in the solution of self-adaptive mesh refinement procedures.

UR - http://www.scopus.com/inward/record.url?scp=0026173586&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026173586&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0026173586

VL - 28

SP - 591

EP - 623

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 3

ER -