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Volume 12, Issue 3
Equivalent a Posteriori Error Estimators for Semilinear Elliptic Equations with Dirac Right-Hand Side

Wenting Mao, Yanping Chen & Haitao Leng

Adv. Appl. Math. Mech., 12 (2020), pp. 835-848.

Published online: 2020-04

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  • 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.

  • AMS Subject Headings

65L10, 65L60, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

maowenting126@163.com (Wenting Mao)

yanpingchen@scnu.edu.cn (Yanping Chen)

lhtdemail@163.com (Haitao Leng)

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@Article{AAMM-12-835, author = {Mao , WentingChen , Yanping and Leng , Haitao}, title = {Equivalent a Posteriori Error Estimators for Semilinear Elliptic Equations with Dirac Right-Hand Side}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {3}, pages = {835--848}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0329}, url = {http://global-sci.org/intro/article_detail/aamm/16426.html} }
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.

Wenting Mao, Yanping Chen & Haitao Leng. (2020). Equivalent a Posteriori Error Estimators for Semilinear Elliptic Equations with Dirac Right-Hand Side. Advances in Applied Mathematics and Mechanics. 12 (3). 835-848. doi:10.4208/aamm.OA-2019-0329
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