Prokopyshyn I. Penalty method based domain decomposition schemes for contact problems of elastic solids

Elliptic variational inequalities for mechanical contact of elastic solids. Methods of nonlinear functional analysis, finite element method, boundary element method. The unique existence of the solution of nonlinear variational equations obtained from variational inequalities by penalty method and its convergence have been proved. Domain decomposition schemes for these equations have been proposed and their convergence have been proved. Numerical implementation techniques based on finite element and boundary element methods in the case of plane deformations have been developed. Application of theoretical results - partial differential equations, numerical methods, application of practical results - mechanical engineering, structural mechanics and biomechanics.