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\(L^{\infty}\)-error estimate for a system of elliptic quasi-variational inequalities with noncoercive operators. (English) Zbl 1060.65065

The considered system plays a fundamental role in solving Hamilton-Jacobi-Bellman equations of stochastic control problems. The coercive case was investigated by M. Boulbrachene and M. Haiour [ibid. 41, 993–1007 (2001; Zbl 0988.65092)].
The results are extended now to the noncoercive case. The finite element method is used and the corresponding \(L^{\infty}\)-error is obtained. The approach is different to the one for the coercive case. It is based to the \(L^{\infty}\)-stability of the solution with respect to the right-hand side and its characterization as the least upper bound of the set of subsolutions.

MSC:

65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
49M15 Newton-type methods

Citations:

Zbl 0988.65092
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References:

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