Displaying similar documents to “Mesh independent superlinear convergence estimates of the conjugate gradient method for some equivalent self-adjoint operators”

Operator preconditioning with efficient applications for nonlinear elliptic problems

Janos Karátson (2012)

Open Mathematics

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This paper is devoted to the numerical solution of nonlinear elliptic partial differential equations. Such problems describe various phenomena in science. An approach that exploits Hilbert space theory in the numerical study of elliptic PDEs is the idea of preconditioning operators. In this survey paper we briefly summarize the main lines of this theory with various applications.

Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations of Elliptic Problems

Paola F. Antonietti, Blanca Ayuso (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we introduce and analyze some non-overlapping multiplicative Schwarz methods for discontinuous Galerkin (DG) approximations of elliptic problems. The construction of the Schwarz preconditioners is presented in a unified framework for a wide class of DG methods. For symmetric DG approximations we provide optimal convergence bounds for the corresponding error propagation operator, and we show that the resulting methods can be accelerated by using suitable Krylov space solvers....

The strengthened C.B.S. inequality constant for second order elliptic partial differential operator and for hierarchical bilinear finite element functions

Ivana Pultarová (2005)

Applications of Mathematics

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We estimate the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for hierarchical bilinear finite element spaces and elliptic partial differential equations with coefficients corresponding to anisotropy (orthotropy). It is shown that there is a nontrivial universal estimate, which does not depend on anisotropy. Moreover, this estimate is sharp and the same as for hierarchical linear finite element spaces.

A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type

Evgenii Pustylnik (2001)

Czechoslovak Mathematical Journal

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The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations.