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

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.

• Keywords

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

65L10, 65L60, 65M70

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 = {Wenting and Mao and maowenting126@163.com and 5549 and School of Mathematical Science, South China Normal University, Guangzhou, Guangdong 520631, China and Wenting Mao and Yanping and Chen and yanpingchen@scnu.edu.cn and 10877 and School of Mathematical Sciences, South China Normal University, Guangzhou, China and Yanping Chen and Haitao and Leng and lhtdemail@163.com and 7334 and School of Mathematical Sciences, South China Normal University, Guangzhou 520631, Guangdong, China and Haitao Leng}, 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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