View : 31 Download: 0

Convergence Analysis of the Standard Central Finite Difference Method for Poisson Equation

Title
Convergence Analysis of the Standard Central Finite Difference Method for Poisson Equation
Authors
Yoon, GangjoonMin, Chohong
Ewha Authors
민조홍윤강준
SCOPUS Author ID
민조홍scopus; 윤강준scopusscopus
Issue Date
2016
Journal Title
JOURNAL OF SCIENTIFIC COMPUTING
ISSN
0885-7474JCR Link1573-7691JCR Link
Citation
vol. 67, no. 2, pp. 602 - 617
Keywords
Convergence analysisFinite difference methodPoisson equationCentral finite difference
Publisher
SPRINGER/PLENUM PUBLISHERS
Indexed
SCIE; SCOPUS WOS scopus
Abstract
We consider the standard central finite difference method for solving the Poisson equation with the Dirichlet boundary condition. This scheme is well known to produce second order accurate solutions. From numerous tests, its numerical gradient was reported to be also second order accurate, but the observation has not been proved yet except for few specific domains. In this work, we first introduce a refined error estimate near the boundary and a discrete version of the divergence theorem. Applying the divergence theorem with the estimate, we prove the second order accuracy of the numerical gradient in arbitrary smooth domains.
DOI
10.1007/s10915-015-0096-2
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
Files in This Item:
There are no files associated with this item.
Export
RIS (EndNote)
XLS (Excel)
XML


qrcode

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

BROWSE