Polynomial of best uniform approximation to 1/x and smoothing in two-level methods

Johannes Kraus, Panayot Vassilevski, Ludmil Zikatanov

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We derive defect correction scheme for constructing the sequence of polynomials of best approximation in the uniform norm to 1/x on a finite interval with positive endpoints. As an application, we consider two-level methods for scalar elliptic partial differential equation (PDE), where the relaxation on the fine grid uses the aforementioned polynomial of best approximation. Based on a new smoothing property of this polynomial smoother that we prove, combined with a proper choice of the coarse space, we obtain as a corollary, that the convergence rate of the resulting two-level method is uniform with respect to the mesh parameters, coarsening ratio and PDE coefficient variation.

Original languageEnglish (US)
Pages (from-to)448-468
Number of pages21
JournalComputational Methods in Applied Mathematics
Volume12
Issue number4
DOIs
StatePublished - Oct 2012

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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