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Nonconforming domain decomposition techniques for linear elasticity. (English) Zbl 1050.74046
From the summary: We present a mortar finite element formulation based on dual basis functions and on a special multigrid method. The starting point for our multigrid method is a symmetric positive definite system on the unconstrained product space. In addition, we introduce a new algorithm for the numerical solution of a nonlinear contact problem between two linear elastic bodies. It is shown that our method can be interpreted as an inexact Dirichlet-Neumann algorithm for nonlinear problems. The boundary data transfer at the contact zone is essential for the algorithm. It is realized by a scaled mass matrix which results from a mortar discretization on non-matching triangulations with dual basis Lagrange multipliers. Numerical results illustrate the performance of our approach in two and three dimensions.

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
74M15 Contact in solid mechanics
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs