A Posteriori Error Estimates of Edge Residual type of Finite Element Method for Nonmonotone Quasi-Linear Elliptic Problems

摘要

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 H~1-norm and L~2-norm. Numerical experiments are provided to illustrate the performance of the proposed error estimators.