Abstract
The main propose of this paper is to provide an error estimate on uniform norm of the parabolic quasi-variational inequalities system related to management of energy production problems, using semi-implicit time scheme with Galerkin spatial methods. Moreover, a new proof of the existence and uniqueness of the solution are given by the introduction of a constructive presented algorithm. Furthermore, an optimally \(L^{\infty }\)-asymptotic behavior in maximum norm is given. The approach is based on the subsolution concept and discrete regularity.
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The authors would like to thank the handling editor and anonymous referee for his/her careful reading and for relevant remarks/suggestions which helped them to improve the paper. The first author gratefully acknowledge Qassim University in Kingdom of Saudi Arabia.
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Boulaaras, S., Bencheikh Le Hocine, M.E.A. & Haiour, M. \(L^{\infty }\)-error estimate of a parabolic quasi-variational inequalities systems related to management of energy production problems via the subsolution concept. Bol. Soc. Mat. Mex. 24, 439–461 (2018). https://doi.org/10.1007/s40590-017-0177-3
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DOI: https://doi.org/10.1007/s40590-017-0177-3
Keywords
- Parabolic quasi-variational inequalities
- Finite element methods
- Subsolutions method
- \(L^{\infty }\)-Asymptotic Behavior