| 中子输运方程误差估计及自适应计算 |
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| 引用本文： | 刘会坡.中子输运方程误差估计及自适应计算[J].计算数学,2015,37(3):264-272. |
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| 作者姓名： | 刘会坡 |
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| 作者单位： | 北京应用物理与计算数学研究所计算物理实验室, 北京 100094 |
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| 基金项目： | 国家自然科学基金(11001027)和中国国家重点基础研究发展计划(2011CB309705)资助项目 |
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| 摘 要： | 本文研究了全离散方法求解二维中子输运方程的有限元自适应算法, 角度变量用离散纵坐标方法展开, 空间变量用间断元方法求解. 基于间断元方法给出了空间离散的残量型后验误差估计. 在后验误差估计的基础上, 我们设计了自适应有限元算法.由残量型后验估计可以给出局部加密网格的自适应算法. 最后, 我们给出了数值算例来验证我们的理论结果.
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| 关 键 词： | 中子输运 间断有限元 后验估计 自适应算法 |
| 收稿时间： | 2015-01-08; |
Error estimates and adaptive algorithm for the neutron transport equations |
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| Liu Huipo.Error estimates and adaptive algorithm for the neutron transport equations[J].Mathematica Numerica Sinica,2015,37(3):264-272. |
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| Authors: | Liu Huipo |
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| Institution: | LCP, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China |
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| Abstract: | In this paper, We establish a posteriori error estimate for a fully discrete method for the two-dimensional neutron transport equations. The discretization is based on the discrete ordinates method for the angular variable and the discontinuous Galerkin finite element method for the space variable. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error to within a given tolerance. The theoretical results are illustrated by a series of numerical experiments. |
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| Keywords: | transport equations discontinuous Galerkin a posteriori error estimators adaptive algorithm |
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