Equivalent a Posteriori Error Estimators for Semilinear Elliptic Equations with Dirac Right-Hand Side

Abstract

In this paper, we consider a semilinear elliptic equation with Dirac right-hand side. An equivalent a posteriori error estimator for the $L^{s}$ norm is obtained. We note that the a posteriori error estimator can be used to design adaptive finite element algorithms. In the end, some examples are provided to examine the quality of the derived estimator.