Based on the variational formulation and penalty method, we have considered the Neumann parallel scheme of the domain decomposition method for the solution of problems of one-sided contact between three-dimensional elastic bodies. We have shown the existence and uniqueness of a solution of the variational problem with penalty and convergence in the penalty parameter. The convergence of this scheme has been proved, and the optimal value of iteration parameter has been determined.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 52, No. 3, pp. 78–89, July–September, 2009.
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Dyyak, I.I., Prokopyshyn, I.I. Convergence of the Neumann parallel scheme of the domain decomposition method for problems of frictionless contact between several elastic bodies. J Math Sci 171, 516–533 (2010). https://doi.org/10.1007/s10958-010-0154-0
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DOI: https://doi.org/10.1007/s10958-010-0154-0