A Posteriori Error Estimates of Edge Residual Type of Finite Element Method for Monotone Nonlinear Elliptic Problems

Abstract:

The edge residual-based a posteriori error estimates of conforming linear finite element method are studied for the monotone nonlinear elliptic problems. Under the assumption of u \in H1，we prove that the edge residuals dominate a posteriori error estimates, and obtain the computable global upper and local lower bounds on the error of the adaptive finite element method in H1 -norm. Up to higher order terms, edge residuals can be a posteriori error estimators. Numerical examples show the efficiency of the edge residual-based a posteriori error estimators.