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On the finite element approximation of elliptic QVIs with noncoercive operators
Author(s) -
Boulbrachene Messaoud
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5345
Subject(s) - mathematics , variational inequality , finite element method , norm (philosophy) , mathematical analysis , pure mathematics , calculus (dental) , law , medicine , physics , dentistry , political science , thermodynamics
In this paper, we extend the approach developed by the author for the standard finite element method in the L ∞ ‐norm of the noncoercive variational inequalities (VI) ( Numer Funct Anal Optim .2015;36:1107‐1121.) to impulse control quasi‐variational inequality (QVI). We derive the optimal error estimate, combining the so‐called Bensoussan‐Lions Algorithm and the concept of subsolutions for VIs.