带损伤弹性反问题的数值分析 |
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引用本文: | 郑聪,程晓良,梁克维. 带损伤弹性反问题的数值分析[J]. 高校应用数学学报(A辑), 2016, 0(4): 476-490. DOI: 10.3969/j.issn.1000-4424.2016.04.010 |
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作者姓名: | 郑聪 程晓良 梁克维 |
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作者单位: | 浙江大学数学科学学院,浙江杭州,310027 |
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基金项目: | 国家自然科学基金(11271258 |
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摘 要: | 考虑一类由椭圆性方程和热传导方程共同来刻画的准静态弹性模型,通过给定观测值来反演边界的牵引力.首先构造一个凸目标泛函,并引入Tikhonov正则化方法,使之极小化得到一个稳定的近似解.再用有限元离散求解,导出误差估计.最后,用数值例子说明算法的可行性和有效性.
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关 键 词: | 变分不等式 有限元方法 误差估计 数值模拟 |
Numerical analysis of inverse elastic problem with damage |
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Abstract: | The quasistatic elastic problem is formulated as an elliptic system for the displace-ments coupled with a parabolic equation for the damage field. The corresponding inverse problem is reformulated as an optimal control problem to find a stable traction, by a given observation data. Firstly, a convex functional is constructed with Tikhonov regularization, and a stable approximation of surface traction is obtained by minimizing it. Then a finite element discretization of the inverse elastic problem is analyzed. Moreover, the error estimation of the numerical solutions is deduced. At last, a numerical algorithm is detailed and three examples illustrate the e?ciency of the algorithm. |
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Keywords: | variational inequality finite element method error estimates numerical simulations |
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