## The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems

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- by James H. Bramble, Joseph E. Pasciak and Jinchao Xu PDF
- Math. Comp.
**51**(1988), 389-414 Request permission

## 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 â€™symmetricâ€™ multigrid schemes. We show that for the variable $\mathcal {V}$-cycle and the $\mathcal {W}$-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 $\mathcal {V}$-cycle algorithm also converges (under appropriate assumptions on the coarsest grid) but at a rate which may deteriorate as the number of levels increases. This deterioration for the $\mathcal {V}$-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.## References

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## Additional Information

- © Copyright 1988 American Mathematical Society
- Journal: Math. Comp.
**51**(1988), 389-414 - MSC: Primary 65N30; Secondary 65F10
- DOI: https://doi.org/10.1090/S0025-5718-1988-0930228-6
- MathSciNet review: 930228