Gradient Recovery-based Error Estimation And The Convergence Analysis Of The Adaptive Finite Element Methods For Elliptic Equations

In this paper,we propose a new gradient recovery-based a posterior error es-timation for elliptic equations with continuous coefficients.Theoretically,the relia-bility and efficiency of the a posteriori error estimator are proved.By applying the reliable and effective error estimator to the adaptive finite element algorithm and combining with appropriate marking strategies,we deduce that the corresponding adaptive algorithm is convergent.Finally,numerical experiments are provided to illustrate the reliability and efficiency of the new recovery type a posteriori error estimation.