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A penalty scheme for monotone systems with interconnected obstacles: convergence and error estimates

Abstract:

We present a novel penalty approach for a class of quasi-variational inequalities (QVIs) involving monotone systems and interconnected obstacles. We show that for any given positive switching cost, the solutions of the penalized equations converge monotonically to those of the QVIs. We estimate the penalization errors and are able to deduce that the optimal switching regions are constructed exactly. We further demonstrate that as the switching cost tends to zero, the QVI degenerates into an e...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1137/18M1207569

Authors


More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Catherine's College
Role:
Author
ORCID:
0000-0003-4027-5298
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
Publisher:
Society for Industrial and Applied Mathematics
Journal:
SIAM Journal on Numerical Analysis More from this journal
Volume:
57
Issue:
4
Pages:
1625–1648
Publication date:
2019-07-09
Acceptance date:
2019-05-22
DOI:
EISSN:
1095-7170
ISSN:
0036-1429
Keywords:
Pubs id:
pubs:1002970
UUID:
uuid:615a0049-e3bd-473b-bc7e-5b30b1134ed8
Local pid:
pubs:1002970
Source identifiers:
1002970
Deposit date:
2019-05-24

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