In this paper, a power penalty approximation method is proposed for solving a mixed quasilinear elliptic complementarity problem. The mixed complementarity problem is first reformulated as a double obstacle quasilinear elliptic variational inequality problem. A nonlinear elliptic partial differential equation is then defined to approximate the resulting variational inequality by using a power penalty approach. The existence and uniqueness of the solution to the partial differential penalty equation are proved. It is shown that, under some mild assumptions, the sequence of solutions to the penalty equations converges to the unique solution of the variational inequality problem as the penalty parameter tends to infinity. The error estimates of the convergence of this penalty approach are also derived. At last, numerical experimental results are presented to show that the power penalty approximation method is efficient and robust.

提出了一种求解混合拟线性椭圆互补问题的幂罚近似方法。首先将混合互补问题重新表述为双障碍拟线性椭圆形变分不等式问题。然后使用功率惩罚方法定义非线性椭圆偏微分方程，以近似所得的变分不等式。证明了偏微分罚分方程解的存在性和唯一性。结果表明，在一些温和的假设下，当惩罚参数趋于无穷大时，惩罚方程的解序列收敛于变分不等式问题的唯一解。还推导了该惩罚方法收敛的误差估计。终于，