Error Analysis and Adaptive Methods of Least Squares Nonconforming Finite Element for the Transport Equations
Year: 2016
Author: Huipo Liu, Shuanghu Wang, Hongbin Han
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 5 : pp. 871–886
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2015.m1104
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 5 : pp. 871–886
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Least squares nonconforming transport equations adaptive methods.