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Error Analysis and Adaptive Methods of Least Squares Nonconforming Finite Element for the Transport Equations

Published online by Cambridge University Press:  08 July 2016

Huipo Liu*
Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
Shuanghu Wang
Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
Hongbin Han
Department of Radiology, Peking University Third Hospital, Beijing 100191, China Beijing Key Lab of Magnetic Resonance Imaging Technology, Beijing 100191, China
*Corresponding author. (H. P. Liu)
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In this paper, we consider a least squares nonconforming finite element of low order for solving the transport equations. We give a detailed overview on the stability and the convergence properties of our considered methods in the stability norm. Moreover, we derive residual type a posteriori error estimates for the least squares nonconforming finite element methods under H–1-norm, which can be used as the error indicators to guide the mesh refinement procedure in the adaptive finite element method. The theoretical results are supported by a series of numerical experiments.

Research Article
Copyright © Global-Science Press 2016 

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