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New convergence estimates for multilevel algorithms for finite-element approximations. (English) Zbl 0808.65129

A new convergence estimate is considered in application to elliptic problems with jump coefficients. If the coefficient has only one jump interface, a uniform rate of convergence is derived. If the coefficient has multi-jump interfaces which meet at only one interior point in the domain, the convergence rate is bounded by \(1 - (CJ)^{-1}\), where \(J\) is the number of levels and \(C\) is the constant independent of the jump. Such approach develops a convergence rate for the multigrid methods for elliptic problems [see J. Wang, SIAM J. Numer. Anal. 30, No. 4, 953-970 (1993; Zbl 0777.65066)].
Reviewer: L.S.Ioffe (Haifa)

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations

Citations:

Zbl 0777.65066
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References:

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