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An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem. (English) Zbl 07166840
Summary: We propose and analyze an interior penalty method for a finite-dimensional large-scale bounded Nonlinear Complementarity Problem (NCP) arising from the discretization of a differential double obstacle problem in engineering. Our approach is to approximate the bounded NCP by a nonlinear algebraic equation containing a penalty function with a penalty parameter \(\mu > 0\). The penalty equation is shown to be uniquely solvable. We also prove that the solution to the penalty equation converges to the exact one at the rate \(\mathcal{O}(\mu^{1 / 2})\) as \(\mu \rightarrow 0\). A smooth Newton method is proposed for solving the penalty equation and it is shown that the linearized system is reducible to two decoupled subsystems. Numerical experiments, performed on some non-trivial test examples, demonstrate the computed rate of convergence matches the theoretical one.

MSC:
35 Partial differential equations
65 Numerical analysis
Software:
MCPLIB
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