New convergence estimates for multilevel algorithms for finite-element approximations
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 \textit{J. Wang}, SIAM J. Numer. Anal. 30, No. 4, 953-970 (1993; Zbl 0777.65066)].
scientific article; zbMATH DE number 643785
scientific article