Volume 10, Issue 3
Optimal Error Estimate of the Penalty FEM for the Stationary Conduction-Convection Problems

Adv. Appl. Math. Mech., 10 (2018), pp. 767-784.

Published online: 2018-10

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• Abstract

In this paper, a penalty finite element method is presented for the two dimensional stationary conduction-convection problems. The existence and the convergence of the penalty stationary conduction-convection formulation are shown. An optimal error estimate of the numerical velocity, pressure and temperature is provided for the penalty finite element method when the parameters $є$ and $h$ are sufficiently small. Our numerical experiments show that our method is effective and our analysis is right.

76M10, 65N12, 65N30, 35K61

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@Article{AAMM-10-767, author = {Lei , YanfangWang , Hongtao and Si , Zhiyong}, title = {Optimal Error Estimate of the Penalty FEM for the Stationary Conduction-Convection Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {3}, pages = {767--784}, abstract = {

In this paper, a penalty finite element method is presented for the two dimensional stationary conduction-convection problems. The existence and the convergence of the penalty stationary conduction-convection formulation are shown. An optimal error estimate of the numerical velocity, pressure and temperature is provided for the penalty finite element method when the parameters $є$ and $h$ are sufficiently small. Our numerical experiments show that our method is effective and our analysis is right.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0103}, url = {http://global-sci.org/intro/article_detail/aamm/12235.html} }
TY - JOUR T1 - Optimal Error Estimate of the Penalty FEM for the Stationary Conduction-Convection Problems AU - Lei , Yanfang AU - Wang , Hongtao AU - Si , Zhiyong JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 767 EP - 784 PY - 2018 DA - 2018/10 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2017-0103 UR - https://global-sci.org/intro/article_detail/aamm/12235.html KW - Conduction-convection problems, penalty finite element method, existence and convergence, error estimates. AB -

In this paper, a penalty finite element method is presented for the two dimensional stationary conduction-convection problems. The existence and the convergence of the penalty stationary conduction-convection formulation are shown. An optimal error estimate of the numerical velocity, pressure and temperature is provided for the penalty finite element method when the parameters $є$ and $h$ are sufficiently small. Our numerical experiments show that our method is effective and our analysis is right.

Yanfang Lei, Hongtao Wang & Zhiyong Si. (2020). Optimal Error Estimate of the Penalty FEM for the Stationary Conduction-Convection Problems. Advances in Applied Mathematics and Mechanics. 10 (3). 767-784. doi:10.4208/aamm.OA-2017-0103
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