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

Huipo Liu ,  Shuanghu Wang and Hongbin Han

10.4208/aamm.2015.m1104

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

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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.

  • History

Published online: 2018-05

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