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

Authors

  • Wenting Mao School of Mathematical Science, South China Normal University, Guangzhou, Guangdong 520631, China
  • Yanping Chen School of Mathematical Sciences, South China Normal University, Guangzhou, China
  • Haitao Leng School of Mathematical Sciences, South China Normal University, Guangzhou 520631, Guangdong, China

DOI:

https://doi.org/10.4208/aamm.OA-2019-0329

Keywords:

Elliptic equation, Dirac, a posteriori error estimator, semilinear, $L^s$ error estimates.

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.

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Published

2020-04-10

Issue

Vol. 12 No. 3 (2020)

Section

Articles