### Abstract

We prove some new estimates for the convergence of multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems. We provide results for the so-called 'symmetric' multigrid schemes. We show that for the variable v-cycle and the m;-cycle schemes, multigrid algorithms with any amount of smoothing on the finest grid converge at a rate that is independent of the number of levels or unknowns, provided that the initial grid is sufficiently fine. We show that the v-cycle algorithm also converges (under appropriate assumptions on the oarsest grid) but at a rate which may deteriorate as the number of levels increases. This deterioration for the m-cycle may occur even in the case of full elliptic regularity. Finally, the results of numerical experiments are given which illustrate the convergence behavior suggested by the theory.

Original language | English (US) |
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Pages (from-to) | 389-414 |

Number of pages | 26 |

Journal | Mathematics of Computation |

Volume | 51 |

Issue number | 184 |

DOIs | |

State | Published - Oct 1988 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

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## Cite this

*Mathematics of Computation*,

*51*(184), 389-414. https://doi.org/10.1090/S0025-5718-1988-0930228-6