Numerical Analysis and Applicable Mathematics
Title
Maximum Norm a Posteriori Error Estimation for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations
Authors
Ying Liang,a Xiaobing Baob and Li-Bin Liu*a
aSchool of Mathematics and Statistics, Nanning Normal University, Nanning 530023, Guangxi, P. R. China
bSchool of Big Data and Artificial Intelligence, Chizhou University, Chizhou 247000, Anhui, P. R.China
*Corresponding author E-mail address: liulibin969@nnnu.edu.cn (Li-Bin Liu)
Article History
Publication details: Received 26th May 2020; Revised 16th June 2020; Accepted 17th June 2020; Published 26th June 2020
Cite this article
Liang Y.; Bao X.; Liu L. B. Maximum Norm a Posteriori Error Estimation for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations. Numer. Anal. Appl. Math., 2020, 1(1), 27-32.
Abstract
In this paper, a system of singularly perturbed semilinear reaction-diffusion equations is discretized on an arbitrary nonuniform mesh using an upwind finite difference scheme. Based on the quadratic polynomial interpolation function, a second-order maximum norm a posteriori error estimation is derived. Then, this bound is used to design an adaptive grid generation algorithm. Numerical results are given to verify the effectiveness of the presented adaptive grid method.
Keywords
singularly perturbed; reaction-diffusion; adaptive grid; a posteriori error estimation
