The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems

James H. Bramble, Joseph E. Pasciak, Jinchao Xu

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56 Scopus citations


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. © 1988 American Mathematical Society.
Original languageEnglish (US)
Pages (from-to)389-414
Number of pages26
JournalMathematics of Computation
Issue number184
StatePublished - Jan 1 1988
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


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