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Main Title: Supraconvergence of a Finite Difference Scheme for Elliptic Boundary Value Problems of the Third Kind in Fractional Order Sobolev Spaces
Author(s): Emmrich, Etienne
Grigorieff, Rolf Dieter
Type: Article
Language Code: en
Abstract: In this paper, we study the convergence of the finite difference discretization of a second order elliptic equation with variable coefficients subject to general boundary conditions. We prove that the scheme exhibits the phenomenon of supraconvergence on nonuniform grids, i.e., although the truncation error is in general of the first order alone, one has second order convergence. All error estimates are strictly local. Another result of the paper is a close relationship between finite difference scheme and linear finite element methods combined with a special kind of quadrature. As a consequence, the results of the paper can be viewed as the introduction of a fully discrete finite element method for which the gradient is superclose. A numerical example is given.
Issue Date: 2006
Date Available: 15-Oct-2018
DDC Class: 510 Mathematik
Subject(s): nonuniform grid
finite differences
supercloseness of gradient
fully discrete linear FEM
Journal Title: Computational methods in applied mathematics
Publisher: De Gruyter
Publisher Place: Berlin
Volume: 6
Issue: 2
Publisher DOI: 10.2478/cmam-2006-0008
Page Start: 154
Page End: 177
EISSN: 1609-9389
ISSN: 1609-4840
Appears in Collections:Inst. Mathematik » Publications

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