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

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• 作者：Owe Axelsson^a ; ^{owea@it.uu.se" class="auth_mail" title="E-mail the corresponding author} ; Já ; nos Kará ; tson^b ; ^c ; ^{karatson@cs.elte.hu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Finite difference method ; Error estimates ; Matrix splitting ; Preconditioning
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：310
• 期：Complete
• 页码：155-164
• 全文大小：452 K

文摘

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.