A posteriori error estimates of edge residual type of finite element method for nonmonotone quasi‐linear elliptic problems. Issue 3 (27th November 2013) - Guo, Liming; Huang, Ziping; Wang, Cheng
<x xml:space="preserve">Abstract</x> 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 H1‐norm and L2‐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