In this paper we study convergence estimates for a multigrid algorithm withsmoothers of successive subspace correction (SSC) type, applied to symmetricelliptic PDEs. First, we revisit a general convergence analysis on a class ofmultigrid algorithms in a fairly general setting, where no regularityassumptions are made on the solution. In this framework, we are able toexplicitly highlight the dependence of the multigrid error bound on the numberof smoothing steps. For the case of no regularity assumptions, this representsa new addition to the existing theory. Then, we analyze successive subspacecorrection smoothing schemes for a set of uniform and local refinementapplications with either nested or non-nested overlapping subdomains. For theseapplications, we explicitly derive bounds for the multigrid error, and identifysufficient conditions for these bounds to be independent of the number ofmultigrid levels. For the local refinement applications, finite element gridswith arbitrary hanging nodes configurations are considered. The analysis ofthese smoothing schemes is cast within the far-reaching multiplicative Schwarzframework.
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