Optimal error estimates of a class of system of two quasi-variational inequalities

Abida Harbi; Nasreddine Nemis; Mohamed Haiour; Abida Harbi; Nasreddine Nemis; Mohamed Haiour

doi:10.3934/math.2021353

AIMS Mathematics

2021, Volume 6, Issue 6: 5977-6001. doi: 10.3934/math.2021353

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Optimal error estimates of a class of system of two quasi-variational inequalities

1.
Department of Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria
2.
Laboratory of Numerical Analysis Optimization and Statistics

Received: 25 December 2020 Accepted: 23 February 2021 Published: 31 March 2021
MSC : 65K15, 65N30, 65N15

In the present paper, the finite element approximation of a class of system of two quasi-variational inequalities with terms sources and obstacles depending on solution is analyzed. An optimal L^∞-error estimate is derived, combining a modified algorithm of Bensoussan-Lions type and standard uniform error estimates known for elliptic variational inequalities (VIs).
Citation: Abida Harbi, Nasreddine Nemis, Mohamed Haiour. Optimal error estimates of a class of system of two quasi-variational inequalities[J]. AIMS Mathematics, 2021, 6(6): 5977-6001. doi: 10.3934/math.2021353

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Abstract

In the present paper, the finite element approximation of a class of system of two quasi-variational inequalities with terms sources and obstacles depending on solution is analyzed. An optimal L^∞-error estimate is derived, combining a modified algorithm of Bensoussan-Lions type and standard uniform error estimates known for elliptic variational inequalities (VIs).

References

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