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

作者：Guo, Liming; Huang, Ziping; Wang, Cheng^*

来源：Numerical Methods for Partial Differential Equations, 2014, 30(3): 813-837.

DOI：10.1002/num.21838

• a posteriori error estimates
• edge residuals
• quasi-linear elliptic problems

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.

• 出版日期2014-5
• 单位同济大学