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Optimal \(L^{\infty}\)-error estimate for variational inequalities with nonlinear source terms. (English) Zbl 1057.65038
Summary: We establish optimal \(L^{\infty}\)-error estimate for a class of variational inequalities (VIs) with nonlinear source term, using a very simple argument mainly based on the discrete \(L^{\infty}\)-stability property with respect to the right-hand side in elliptic VIs. We also show that the same approach extends to the corresponding noncoercive problems and optimal uniform convergence order is obtained as well.

MSC:
65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
49M25 Discrete approximations in optimal control
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