Accessible Requires Authentication Published by De Gruyter January 1, 2012

Polynomial of Best Uniform Approximation to and Smoothing in Two-level Methods

Johannes Kraus, Panayot Vassilevski and Ludmil Zikatanov

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.

Received: 2012-05-08
Revised: 2012-08-28
Accepted: 2012-08-29
Published Online: 2012
Published in Print: 2012

© Institute of Mathematics, NAS of Belarus