| 半线性椭圆问题的非精确自适应有限元方法 |
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| 引用本文： | 张庆敏,郭利明.半线性椭圆问题的非精确自适应有限元方法[J].信阳师范学院学报(自然科学版),2021(1):11-15,144. |
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| 作者姓名： | 张庆敏 郭利明 |
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| 作者单位： | 1.信阳师范学院旅游学院;2.信阳师范学院数学与统计学院 |
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| 摘 要： | 考虑一类半线性椭圆问题的非精确自适应有限元方法.该算法在初始网格需要精确求解,而在其余网格只需要对上一步的近似解进行一次牛顿更新.利用有限元方法的精确解和非精确解之间的超逼近性质,给出该方法的先验和后验误差估计,最后通过具体算例来验证该理论的正确性和该方法的有效性.
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| 关 键 词： | 非精确 自适应有限元 先验误差估计 后验误差估计 半线性 |
The Inexact Adaptive Finite Element Method for Semilinear Elliptic Problems |
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| Institution: | ,College of Tourism,Xinyang Normal University,College of Mathematics and Statistics,Xinyang Normal University |
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| Abstract: | A type of inexact adaptive finite element method for semilinear elliptic problems is considered.The algorithm needs an accurate solution on the coarsest level,and the remaining levels involve only single Newton updates to the previous approximate solution.By using the super approximation property between the exact and inexact solutions of finite element method,the priori and posteriori error estimates of the proposed method are given,and the numerical experiments are provided to illustrate the theory and the algorithm. |
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| Keywords: | inexact adaptive finite element method priori error estimates posteriori error estimates semilinear |
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