# L∞ Error Estimate for the Noncoercive Impulse Control QVI: A New Approach

Research output: Contribution to journalArticle

### Abstract

In this paper, we introduce a new method to analyze the convergence of the standard finite element method for the noncoercive impulse control quasi-variational inequality (QVI). L convergence of the approximation is derived as a result of the geometrical convergence of a Bensoussan–Lions algorithm type and uniform error estimate between the continuous algorithm and its finite element counterpart. This approach is completely different from the one inroduced in  as it enables us to derive the error estimate through a computational iterative scheme.

Original language English 1-8 8 Computational Mathematics and Modeling https://doi.org/10.1007/s10598-016-9338-x Accepted/In press - Aug 9 2016

### Fingerprint

Impulse Control
Quasi-variational Inequalities
Error Estimates
Uniform Estimates
Iterative Scheme
Finite element method
Finite Element Method
Finite Element
Approximation

### Keywords

• algorithm
• finite element
• L error estimate
• quasi-variational inequalities

### ASJC Scopus subject areas

• Computational Mathematics

### Cite this

In: Computational Mathematics and Modeling, 09.08.2016, p. 1-8.

Research output: Contribution to journalArticle

title = "L∞ Error Estimate for the Noncoercive Impulse Control QVI: A New Approach",
abstract = "In this paper, we introduce a new method to analyze the convergence of the standard finite element method for the noncoercive impulse control quasi-variational inequality (QVI). L∞ convergence of the approximation is derived as a result of the geometrical convergence of a Bensoussan–Lions algorithm type and uniform error estimate between the continuous algorithm and its finite element counterpart. This approach is completely different from the one inroduced in  as it enables us to derive the error estimate through a computational iterative scheme.",
keywords = "algorithm, finite element, L error estimate, quasi-variational inequalities",
author = "M. Boulbrachene",
year = "2016",
month = "8",
day = "9",
doi = "10.1007/s10598-016-9338-x",
language = "English",
pages = "1--8",
journal = "Computational Mathematics and Modeling",
issn = "1046-283X",
publisher = "Springer New York",

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T1 - L∞ Error Estimate for the Noncoercive Impulse Control QVI

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AU - Boulbrachene, M.

PY - 2016/8/9

Y1 - 2016/8/9

N2 - In this paper, we introduce a new method to analyze the convergence of the standard finite element method for the noncoercive impulse control quasi-variational inequality (QVI). L∞ convergence of the approximation is derived as a result of the geometrical convergence of a Bensoussan–Lions algorithm type and uniform error estimate between the continuous algorithm and its finite element counterpart. This approach is completely different from the one inroduced in  as it enables us to derive the error estimate through a computational iterative scheme.

AB - In this paper, we introduce a new method to analyze the convergence of the standard finite element method for the noncoercive impulse control quasi-variational inequality (QVI). L∞ convergence of the approximation is derived as a result of the geometrical convergence of a Bensoussan–Lions algorithm type and uniform error estimate between the continuous algorithm and its finite element counterpart. This approach is completely different from the one inroduced in  as it enables us to derive the error estimate through a computational iterative scheme.

KW - algorithm

KW - finite element

KW - L error estimate

KW - quasi-variational inequalities

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JO - Computational Mathematics and Modeling

JF - Computational Mathematics and Modeling

SN - 1046-283X

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