\(L^{\infty}\)-error estimate for a system of elliptic quasi-variational inequalities with noncoercive operators
type: Item
instance of: scholarly article
title: \(L^{\infty}\)-error estimate for a system of elliptic quasi-variational inequalities with noncoercive operators
zbMATH Open document ID: 1060.65065
DOI: 10.1016/S0898-1221(03)00072-5
publication date: 2004-08-06T00:00:00Z
review text: The considered system plays a fundamental role in solving Hamilton-Jacobi-Bellman equations of stochastic control problems. The coercive case was investigated by \textit{M. Boulbrachene} and \textit{M. Haiour} [ibid. 41, 993--1007 (2001; Zbl 0988.65092)]. The results are extended now to the noncoercive case. The finite element method is used and the corresponding \(L^{\infty}\)-error is obtained. The approach is different to the one for the coercive case. It is based to the \(L^{\infty}\)-stability of the solution with respect to the right-hand side and its characterization as the least upper bound of the set of subsolutions.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49M15
zbMATH DE Number: 2082208
zbMATH Keywords: quasi-variational inequalities
zbMATH Keywords: finite element method
zbMATH Keywords: subsolutions
zbMATH Keywords: Hamilton-Jacobi-Bellman equations
zbMATH Keywords: stochastic control problems
zbMATH Keywords: \(L^{\infty}\)-stability
zbMATH Keywords: \(L^{\infty}\)-error estimate
author: M. Boulbrachene
reviewed by: Viorel Arnăutu
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2082208