Error Estimates on Arbitrary Grids for a 2nd-order Mimetic Discretization of Boundary-value Problems for Linear Odes

We obtain sharp pointwise 2nd-order estimates for both solution and derivative errors on arbitrary grids for a mimetic finite-difference approximation to solutions of one-dimensional linear boundary-value problems with separated boundary conditions. Although the scheme considered is formally inconsi...

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Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 9; no. 2; pp. 192 - 202
Main Authors Zingano, J.P., Steinberg, S.L.
Format Journal Article
LanguageEnglish
Published De Gruyter 2009
Subjects
boundary-value problems
error analysis
irregular grids
mimetic methods
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Summary:We obtain sharp pointwise 2nd-order estimates for both solution and derivative errors on arbitrary grids for a mimetic finite-difference approximation to solutions of one-dimensional linear boundary-value problems with separated boundary conditions. Although the scheme considered is formally inconsistent with the differential equation, it turns out to possess nice convergence properties which make it a good alternative to more standard, consistent discretizations of similar arithmetic complexity, particularly with respect to derivative errors.
ISSN:1609-4840
1609-9389
DOI:10.2478/cmam-2009-0011