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

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  • Rui Ding

    (Soochow University)

  • Chaoren Ding

    (Soochow University)

  • Quan Shen

    (Soochow University)

Abstract

In this paper, the interpolating element-free Galerkin method is presented for the p-Laplace double obstacle mixed complementarity problem when $$1 2$$ 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 $$1 2$$ 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 $$\lambda $$ λ and p. For different p, the method that how to choose the optimal k and $$\lambda $$ λ is also given. Numerical examples verify error estimates and illustrate the influence of each parameter on the solution.

Suggested Citation

  • Rui Ding & Chaoren Ding & Quan Shen, 2023. "The interpolating element-free Galerkin method for the p-Laplace double obstacle mixed complementarity problem," Journal of Global Optimization, Springer, vol. 86(3), pages 781-820, July.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:3:d:10.1007_s10898-022-01260-x
    DOI: 10.1007/s10898-022-01260-x
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    References listed on IDEAS

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    1. S. A. Gabriel, 1998. "An NE/SQP Method for the Bounded Nonlinear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 493-506, May.
    2. Yarui Duan & Song Wang & Yuying Zhou, 2021. "A power penalty approach to a mixed quasilinear elliptic complementarity problem," Journal of Global Optimization, Springer, vol. 81(4), pages 901-918, December.
    3. S. Wang & X. Q. Yang & K. L. Teo, 2006. "Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 227-254, May.
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