### Abstract

Language | English |
---|---|

Pages | 2427–2451 |

Number of pages | 25 |

Journal | SIAM Journal on Numerical Analysis |

Volume | 54 |

Issue number | 4 |

Early online date | 16 Aug 2016 |

DOIs | |

Publication status | E-pub ahead of print - 16 Aug 2016 |

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### Keywords

- algebraic flux correction method
- linear boundary value problem
- well-posedness
- discrete maximum principle
- convergence analysis
- convection–diffusion–reaction equations

### Cite this

*SIAM Journal on Numerical Analysis*,

*54*(4), 2427–2451. https://doi.org/10.1137/15M1018216

}

*SIAM Journal on Numerical Analysis*, vol. 54, no. 4, pp. 2427–2451. https://doi.org/10.1137/15M1018216

**Analysis of algebraic flux correction schemes.** / Barrenechea, Gabriel; Volker, John; Knobloch, Petr.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Analysis of algebraic flux correction schemes

AU - Barrenechea, Gabriel

AU - Volker, John

AU - Knobloch, Petr

PY - 2016/8/16

Y1 - 2016/8/16

N2 - A family of algebraic flux correction schemes for linear boundary value problems in any space dimension is studied. These methods’ main feature is that they limit the fluxes along each one of the edges of the triangulation, and we suppose that the limiters used are symmetric. For an abstract problem, the existence of a solution, existence and uniqueness of the solution of a linearized problem, and an a priori error estimate, are proved under rather general assumptions on the limiters. For a particular (but standard in practice) choice of the limiters, it is shown that a local discrete maximum principle holds. The theory developed for the abstract problem is applied to convection–diffusion–reaction equations, where in particular an error estimate is derived. Numerical studies show its sharpness.

AB - A family of algebraic flux correction schemes for linear boundary value problems in any space dimension is studied. These methods’ main feature is that they limit the fluxes along each one of the edges of the triangulation, and we suppose that the limiters used are symmetric. For an abstract problem, the existence of a solution, existence and uniqueness of the solution of a linearized problem, and an a priori error estimate, are proved under rather general assumptions on the limiters. For a particular (but standard in practice) choice of the limiters, it is shown that a local discrete maximum principle holds. The theory developed for the abstract problem is applied to convection–diffusion–reaction equations, where in particular an error estimate is derived. Numerical studies show its sharpness.

KW - algebraic flux correction method

KW - linear boundary value problem

KW - well-posedness

KW - discrete maximum principle

KW - convergence analysis

KW - convection–diffusion–reaction equations

UR - http://epubs.siam.org/loi/sjnaam

U2 - 10.1137/15M1018216

DO - 10.1137/15M1018216

M3 - Article

VL - 54

SP - 2427

EP - 2451

JO - SIAM Journal on Numerical Analysis

T2 - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 4

ER -