### Abstract

We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to achieve convergence is uniformly bounded independently of the characteristic size of the underlying partition. We also show that the resulting scheme provides a uniform preconditioner with respect to the number of degrees of freedom. Numerical results that validate the theory are also presented.

Original language | English (US) |
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Pages (from-to) | 2674-2687 |

Number of pages | 14 |

Journal | Computers and Mathematics with Applications |

Volume | 70 |

Issue number | 11 |

DOIs | |

State | Published - Dec 2015 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*Computers and Mathematics with Applications*,

*70*(11), 2674-2687. https://doi.org/10.1016/j.camwa.2015.06.010

}

*Computers and Mathematics with Applications*, vol. 70, no. 11, pp. 2674-2687. https://doi.org/10.1016/j.camwa.2015.06.010

**A two-level method for mimetic finite difference discretizations of elliptic problems.** / Antonietti, Paola F.; Verani, Marco; Zikatanov, Ludmil.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A two-level method for mimetic finite difference discretizations of elliptic problems

AU - Antonietti, Paola F.

AU - Verani, Marco

AU - Zikatanov, Ludmil

PY - 2015/12

Y1 - 2015/12

N2 - We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to achieve convergence is uniformly bounded independently of the characteristic size of the underlying partition. We also show that the resulting scheme provides a uniform preconditioner with respect to the number of degrees of freedom. Numerical results that validate the theory are also presented.

AB - We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to achieve convergence is uniformly bounded independently of the characteristic size of the underlying partition. We also show that the resulting scheme provides a uniform preconditioner with respect to the number of degrees of freedom. Numerical results that validate the theory are also presented.

UR - http://www.scopus.com/inward/record.url?scp=84947869249&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947869249&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2015.06.010

DO - 10.1016/j.camwa.2015.06.010

M3 - Article

AN - SCOPUS:84947869249

VL - 70

SP - 2674

EP - 2687

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 11

ER -