Adaptive finite element analysis for semilinear elliptic problems

Abstract

In this paper, without using the uniform boundedness of finite element approximations, we derive both a priori and a posteriori finite element error estimates for a class of semilinear elliptic problems, based on which we analyze an adaptive finite element method to approximate the solutions of this kind of semilinear problems. In particular, we obtain the convergence rate and complexity of the adaptive finite element method.