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

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

Author Details

Huipo Liu

Shuanghu Wang

Hongbin Han