TY - JOUR T1 - Equivalent a Posteriori Error Estimators for Semilinear Elliptic Equations with Dirac Right-Hand Side AU - Mao , Wenting AU - Chen , Yanping AU - Leng , Haitao JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 835 EP - 848 PY - 2020 DA - 2020/04 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0329 UR - https://global-sci.org/intro/article_detail/aamm/16426.html KW - Elliptic equation, Dirac, a posteriori error estimator, semilinear, $L^s$ error estimates. AB -

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.