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

Rui Ding (), Chaoren Ding () and Quan Shen ()
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Rui Ding: Soochow University
Chaoren Ding: Soochow University
Quan Shen: Soochow University

Journal of Global Optimization, 2023, vol. 86, issue 3, No 10, 820 pages

Abstract: 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.

Keywords: Interpolating element-free Galerkin method; p-Laplace; Double obstacle mixed complementarity problem; Power penalty method (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01260-x

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