Error Analysis and Adaptive Methods of Least Squares Nonconforming Finite Element for the Transport Equations. Issue 5 (8th July 2016)

• Record Type: Journal Article
• Authors: Liu, Huipo; Wang, Shuanghu; Han, Hongbin
• Is Part Of: Advances in applied mathematics and mechanics. Volume 8:Issue 5(2016)
• Page Start: 871
• Page End: 886
• Publication Date: 2016-07-08
• Subjects: 65N30; Least squares, -- nonconforming, -- transport equations, -- adaptive methods; Engineering mathematics -- Periodicals; Mechanics -- Periodicals; 620.00151825
• DOI: 10.4208/aamm.2015.m1104
• Languages: English
• ISSNs: 2070-0733

Abstract

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.