This paper presents a concurrent global-local numerical method for solving multiscale parabolic equations in divergence form. The proposed method employs hybrid coefficient to provide accurate macroscopic information while preserving essential microscopic details within specified local defects. Both the macroscopic and microscopic errors have been improved compared with existing results, eliminating the factor of Δt^{-1/2} when the diffusion coefficient is time-independent. Numerical experiments demonstrate that the proposed method effectively captures both global and local solution behaviours.
Publication:
IMA JOURNAL OF NUMERICAL ANALYSIS
http://dx.doi.org/10.1093/imanum/drag049
Author:
YULEI LIAO
Department of Mathematics, Faculty of Science, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076, Singapore
YANG LIU
State Key Laboratory of Mathematical Sciences, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, No. 55 Zhongguancun East Road, Beijing 100190, China
School of Mathematical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049, China
PINGBING MING
State Key Laboratory of Mathematical Sciences, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, No. 55 Zhongguancun East Road, Beijing 100190, China
School of Mathematical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049, China
Corresponding author
Email: mpb@lsec.cc.ac.cn
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