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Convergence Analysis in the Maximum Norm of the Numerical Gradient of the Shortley-Weller Method

Title
Convergence Analysis in the Maximum Norm of the Numerical Gradient of the Shortley-Weller Method
Authors
Seo, JiwonHa, Seung-yealMin, Chohong
Ewha Authors
민조홍
SCOPUS Author ID
민조홍scopus
Issue Date
2018
Journal Title
JOURNAL OF SCIENTIFIC COMPUTING
ISSN
0885-7474JCR Link1573-7691JCR Link
Citation
vol. 74, no. 2, pp. 631 - 639
Keywords
Shortley-WellerFinite difference methodSuper-convergenceConvergence analysis
Publisher
SPRINGER/PLENUM PUBLISHERS
Indexed
SCIE; SCOPUS WOS scopus
Abstract
The Shortley-Weller method is a standard central finite-difference-method for solving the Poisson equation in irregular domains with Dirichlet boundary conditions. It is well known that the Shortley-Weller method produces second-order accurate solutions and it has been numerically observed that the solution gradients are also second-order accurate; a property known as super-convergence. The super-convergence was proved in the norm in Yoon and Min (J Sci Comput 67(2):602-617, 2016). In this article, we present a proof for the super-convergence in the norm.
DOI
10.1007/s10915-017-0458-z
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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