| 一类非线性变分问题的有限元逼近及其应用 |
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| 引用本文： | 蒲春生,张绍槐. 一类非线性变分问题的有限元逼近及其应用[J]. 西安石油大学学报(自然科学版), 1991, 0(4) |
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| 作者姓名： | 蒲春生 张绍槐 |
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| 作者单位： | 西南石油学院，西安石油学院 |
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| 摘 要： | 本文应用不动点原理和有限元基本理论,提出了比较广泛一类非线性变分问题的有限元逼近,这种方法可以用来求解数学物理中经常出现的一类非线性偏微分方程(组),采用迭代技术进行线性化,使求解大大简化。证明了连续解和有限元解的存在唯一性,得到了敛速估计,并给出了在数学物理中的应用实例。
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| 关 键 词： | 数学物理 非线性变分 迭代线性化 有限元逼近 |
The Finite Element Approximation of a Nonlinear Variation Problem and Its Application |
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| Pu Chusheng. The Finite Element Approximation of a Nonlinear Variation Problem and Its Application[J]. Journal of Xian Shiyou University, 1991, 0(4) |
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| Authors: | Pu Chusheng |
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| Affiliation: | Pu Chusheng (Southwest Petroleum Institute)Zhang Shao(Xi'an Petroleum Institute) |
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| Abstract: | This paper is devoted to the finite element approximation of a rather general nonlinear variation problem. The existence, uniqueness and convergence of the continuous solution and the unite element solution were obtained by combining the fixed poing principle with FEM theory. BY means of iterative technique, the problem was linearized and the solving procedure was greatly simplified. The convergent rate of the approximation solution and several examples of its applieation in mathematical physies were given. |
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| Keywords: | mathematical physics nonlinear variation iteration linearization finite clement approximation |
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