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

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  08 July 2016

Huipo Liu ,
Shuanghu Wang  and
Hongbin Han
Huipo Liu*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
Shuanghu Wang
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
Hongbin Han
Affiliation:
Department of Radiology, Peking University Third Hospital, Beijing 100191, China Beijing Key Lab of Magnetic Resonance Imaging Technology, Beijing 100191, China
*
*Corresponding author. Email:liuhuipo@amss.ac.cn (H. P. Liu)
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Abstract

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.

Keywords

Least squaresnonconformingtransport equationsadaptive methods

MSC classification

Secondary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 5 , October 2016 , pp. 871 - 886
Copyright
Copyright © Global-Science Press 2016 

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