Geodesic
A modified dual scheme for solving an elastic crack problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 1, pp. 47-58

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The dual scheme for solving a crack problem in terms of displacements is considered. The dual solution method is based on a modified Lagrangian functional. In addition, the method convergence is investigated under natural assumptions on $H^1$-regularity of the crack problem solution. The duality relation for the primal and dual problems has been proposed. 
@article{SJVM_2017_20_1_a4,
     author = {R. V. Namm and G. I. Tsoy},
     title = {A modified dual scheme for solving an elastic crack problem},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {47--58},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2017_20_1_a4/}
}
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R. V. Namm; G. I. Tsoy. A modified dual scheme for solving an elastic crack problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 1, pp. 47-58. http://geodesic.mathdoc.fr/item/SJVM_2017_20_1_a4/