TY - JOUR
T1 - Convergence Analysis of the Standard Central Finite Difference Method for Poisson Equation
AU - Yoon, Gangjoon
AU - Min, Chohong
N1 - Funding Information:
This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827).
Publisher Copyright:
© 2015, Springer Science+Business Media New York.
PY - 2016/5/1
Y1 - 2016/5/1
N2 - 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.
AB - 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.
KW - Central finite difference
KW - Convergence analysis
KW - Finite difference method
KW - Poisson equation
UR - http://www.scopus.com/inward/record.url?scp=84940985962&partnerID=8YFLogxK
U2 - 10.1007/s10915-015-0096-2
DO - 10.1007/s10915-015-0096-2
M3 - Article
AN - SCOPUS:84940985962
VL - 67
SP - 602
EP - 617
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
SN - 0885-7474
IS - 2
ER -