The interpolating element-free Galerkin method for the

In this paper, the interpolating element-free Galerkin method is presented for the p -Laplace double obstacle mixed complementarity problem when 1 < p < 2 and p > 2 . First, a nonlinear power penalty equation is obtained by a power penalty approximation method and the existence and uniqueness of the solution to the power penalty equation are proved when 1 < p < 2 and p > 2 . The convergence of the power penalty solution to the original problem and the penalty estimates are analyzed. Second, the interpolating element-free Galerkin method is constructed for the nonlinear power penalty equation. The numerical implementation is introduced in detail and the convergence of the interpolating element-free Galerkin method is also given. Error estimates indicate that the convergence order depends on not only the spatial step h and the number of bases functions m in the interpolating element-free Galerkin method, but also the index k in the penalty term, the penalty factor λ and p . For different p , the method that how to choose the optimal k and λ is also given. Numerical examples verify error estimates and illustrate the influence of each parameter on the solution.