TY - GEN
T1 - Stability and error analysis of nodal expansion method for convection-diffusion equation
AU - Deng, Zhihong
AU - Rizwan-uddin,
AU - Li, Fu
AU - Sun, Yuliang
PY - 2012
Y1 - 2012
N2 - The development, and stability and error analyses of nodal expansion method (NEM) for one dimensional steady-state convection diffusion equation is presented. Following the traditional procedure to develop NEM, the discrete formulation of the convection-diffusion equation, which is similar to the standard finite difference scheme, is derived. The method of discrete perturbation analysis is applied to this discrete form to study the stability of the NEM. The scheme based on the NEM is found to be stable for local Peclet number less than 4.644. A maximum principle is proved for the NEM scheme, followed by an error analysis carried out by applying the Maximum principle together with a carefully constructed comparison function. The scheme for the convection diffusion equation is of second-order. Numerical experiments are carried and the results agree with the conclusions of the stability and error analyses.
AB - The development, and stability and error analyses of nodal expansion method (NEM) for one dimensional steady-state convection diffusion equation is presented. Following the traditional procedure to develop NEM, the discrete formulation of the convection-diffusion equation, which is similar to the standard finite difference scheme, is derived. The method of discrete perturbation analysis is applied to this discrete form to study the stability of the NEM. The scheme based on the NEM is found to be stable for local Peclet number less than 4.644. A maximum principle is proved for the NEM scheme, followed by an error analysis carried out by applying the Maximum principle together with a carefully constructed comparison function. The scheme for the convection diffusion equation is of second-order. Numerical experiments are carried and the results agree with the conclusions of the stability and error analyses.
UR - http://www.scopus.com/inward/record.url?scp=84869053226&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84869053226&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84869053226
SN - 9781622762101
T3 - International Congress on Advances in Nuclear Power Plants 2012, ICAPP 2012
SP - 2248
EP - 2257
BT - International Congress on Advances in Nuclear Power Plants 2012, ICAPP 2012
T2 - International Congress on Advances in Nuclear Power Plants 2012, ICAPP 2012
Y2 - 24 June 2012 through 28 June 2012
ER -