The element-free Galerkin method for the variational–hemivariational inequality of the dynamic Signorini–Tresca contact problems with friction in elastic materials

The element-free Galerkin method is presented for the variational–hemivariational inequality of the dynamic Signorini–Tresca contact problems with friction in elastic materials. The Dirichlet boundary conditions and the constrained conditions are imposed by the penalty method. The error estimates of the element-free Galerkin method indicate that the convergence order depends on the spatial step, the time step, the largest degree of basis functions in the moving least-squares approximation and the penalty factor. Numerical examples verify our theoretical results.