Geodesic
On the dual method for a model problem with a crack
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 36-43

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The dual method based on a modified Lagrangian functional is applied to a model problem with a crack. The convergence of the method is investigated under the assumption that the solution of the primal problem is $H^1$-regular. The duality relation is established for the primal and dual problems.
Keywords: model problem with a crack, dual method, modified Lagrangian functional, sensitivity functional. 
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E. M. Vikhtenko; R. V. Namm. On the dual method for a model problem with a crack. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 36-43. http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a3/