Discretization error estimates in maximum norm for convergent splittings of matrices with a monotone preconditioning part

Owe Axelsson, J. Karátson

Research output: Contribution to journalArticle

Abstract

For finite difference matrices that are monotone, a discretization error estimate in maximum norm follows from the truncation errors of the discretization. It enables also discretization error estimates for derivatives of the solution. These results are extended to convergent operator splittings of the difference matrix where the major, preconditioning part is monotone but the whole operator is not necessarily monotone.

Original languageEnglish
JournalJournal of Computational and Applied Mathematics
DOIs
Publication statusAccepted/In press - Jan 20 2016

Fingerprint

Maximum Norm
Discretization Error
Preconditioning
Difference Matrix
Error Estimates
Monotone
Operator Splitting
Truncation Error
Finite Difference
Discretization
Derivatives
Derivative
Operator

Keywords

  • Error estimates
  • Finite difference method
  • Matrix splitting
  • Preconditioning

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

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abstract = "For finite difference matrices that are monotone, a discretization error estimate in maximum norm follows from the truncation errors of the discretization. It enables also discretization error estimates for derivatives of the solution. These results are extended to convergent operator splittings of the difference matrix where the major, preconditioning part is monotone but the whole operator is not necessarily monotone.",
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KW - Matrix splitting

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