An Optimal A Priori Error Estimate for Nonlinear Multibody Contact Problems

Nonconforming domain decomposition methods provide a powerful tool for the numerical approximation of partial differential equations. For the discretization of a nonlinear multibody contact problem, we use linear mortar finite elements based on dual Lagrange multipliers. Under some regularity assumptions on the solution, an optimal convergence order of $h^{0.5+\nu}$, $0 < \nu\leq 0.5$, can be established in two dimensions (2D) and three dimensions (3D). Compared with a standard linear saddle point formulation, two additional terms which provide a measure for the nonconformity and the nonlinearity of the approach have to be taken in account. Numerical examples illustrating the performance of the nonconforming method and confirming our theoretical result are presented.