A posteriori error estimates of edge residual type of finite element method for nonmonotone quasi‐linear elliptic problems. Issue 3 (27th November 2013)

• Record Type: Journal Article
• Authors: Guo, Liming; Huang, Ziping; Wang, Cheng
• Is Part Of: Numerical methods for partial differential equations. Volume 30:Issue 3(2014:May)
• Page Start: 813
• Page End: 837
• Publication Date: 2013-11-27
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21838
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>In this article, we study the edge residual‐based a posteriori error estimates of conforming linear finite element method for nonmonotone quasi‐linear elliptic problems. It is proven that edge residuals dominate a posteriori error estimates. Up to higher order perturbations, edge residuals can act as a posteriori error estimators. The global reliability and local efficiency bounds are established both in <italic>H</italic>¹‐norm and <italic>L</italic>²‐norm. Numerical experiments are provided to illustrate the performance of the proposed error estimators. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 813–837, 2014</p> </abstract>