Resolvent Estimate in L_p for Discretisations of Second Order Ordinary Differential Operators on Variable Grids

In this paper, a resolvent estimate is proved for discretisations of second order ordinary differential operators subject to Dirichlet boundary conditions on a finite or infinite interval. As a discretisation method, a fully discrete Galerkin method using continuous splines of order r > 2 on a lo...

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Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 3; no. 2; pp. 235 - 252
Main Author Grigorieff, R. D.
Format Journal Article
LanguageEnglish
Published De Gruyter 2003
Subjects
finite element
fully discrete method
higher order splines
locally quasi-uniform grid
maximum-norm
resolvent estimate
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ISSN1609-4840
1609-9389
DOI10.2478/cmam-2003-0016

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Summary:In this paper, a resolvent estimate is proved for discretisations of second order ordinary differential operators subject to Dirichlet boundary conditions on a finite or infinite interval. As a discretisation method, a fully discrete Galerkin method using continuous splines of order r > 2 on a locally quasi-uniform grid is considered. As a byproduct, an a priori estimate for the discretised differential operator is obtained.
ISSN:1609-4840
1609-9389
DOI:10.2478/cmam-2003-0016