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Volume 8, Issue 5
Error Analysis and Adaptive Methods of Least Squares Nonconforming Finite Element for the Transport Equations

Huipo Liu, Shuanghu Wang & Hongbin Han

DOI: 10.4208/aamm.2015.m1104

Adv. Appl. Math. Mech., 8 (2016), pp. 871-886.

Published online: 2018-05

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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 squares, nonconforming, transport equations, adaptive methods.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-871, author = {Liu , HuipoWang , Shuanghu and Han , Hongbin}, title = {Error Analysis and Adaptive Methods of Least Squares Nonconforming Finite Element for the Transport Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {5}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1104}, url = {http://global-sci.org/intro/article_detail/aamm/12121.html} }
TY - JOUR T1 - Error Analysis and Adaptive Methods of Least Squares Nonconforming Finite Element for the Transport Equations AU - Liu , Huipo AU - Wang , Shuanghu AU - Han , Hongbin JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 871 EP - 886 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2015.m1104 UR - https://global-sci.org/intro/article_detail/aamm/12121.html KW - Least squares, nonconforming, transport equations, adaptive methods. AB -

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.

Liu , HuipoWang , Shuanghu and Han , Hongbin. (2018). Error Analysis and Adaptive Methods of Least Squares Nonconforming Finite Element for the Transport Equations. Advances in Applied Mathematics and Mechanics. 8 (5). 871-886. doi:10.4208/aamm.2015.m1104
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