Geodesic
A dual method for solving the equilibrium problem of a body containing a thin defect
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 26 (2023) no. 2, pp. 183-198 Cet article a éte moissonné depuis la source Math-Net.Ru

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An equilibrium problem of a two-dimensional body with a thin defect whose properties are characterized by a fracture parameter is considered. The problem is discretized, and an approximation accuracy theorem is proved. To solve the problem, a dual method based on a modified Lagrange functional is used. In computational experiments, when solving the direct problem, a generalized Newton's method is used with a step satisfying Armijo's condition. 
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A. Zhiltsov; N. N. Maksimova. A dual method for solving the equilibrium problem of a body containing a thin defect. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 26 (2023) no. 2, pp. 183-198. http://geodesic.mathdoc.fr/item/SJVM_2023_26_2_a4/

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