The interpolating element-free Galerkin method for the p-Laplace double obstacle mixed complementarity problem

In this paper, the interpolating element-free Galerkin method is presented for thep-Laplace double obstacle mixed complementarity problem when 1 < p < 2 and p > 2. First, anonlinear power penalty equation is obtained by a power penalty approximation method andthe existence and uniqueness of the solution to the power penalty equation are proved when1 < p < 2andp > 2. The convergence of the power penalty solution to the original prob-lem and the penalty estimates are analyzed. Second, the interpolating element-free Galerkin method is constructed for the nonlinear power penalty equation. The numerical implemen-tation 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 notonly the spatial stephand the number of bases functionsmin the interpolating element-free Galerkin method, but also the index k in the penalty term, the penalty factor lambda andp.Fordifferentp, the method that how to choose the optimalkand lambda is also given. Numerical examples verify error estimates and illustrate the influence of each parameter on the solution.