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

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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 \(\lambda \) and p. For different p, the method that how to choose the optimal k and \(\lambda \) is also given. Numerical examples verify error estimates and illustrate the influence of each parameter on the solution.

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Authors and Affiliations

  1. School of Mathematical Sciences, Soochow University, Suzhou, 215006, China

    Rui Ding & Chaoren Ding

  2. School of Rail Transportation, Soochow University, Suzhou, 215131, China

    Quan Shen

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  1. Rui Ding
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  2. Chaoren Ding
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This work was supported by the National Natural Science Foundation of China (Nos. 11401416 and 11771319).

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Ding, R., Ding, C. & Shen, Q. The interpolating element-free Galerkin method for the p-Laplace double obstacle mixed complementarity problem. J Glob Optim 86, 781–820 (2023). https://doi.org/10.1007/s10898-022-01260-x

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